Номер 2, страница 88 - гдз по физике 9 класс учебник Изергин

Глава III. Механические колебания и волны. Параграф 18. Графическое описание колебательного движения - номер 2, страница 88.

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App\Models\Task {#1030 // resources/views/models/task/default.blade.php
  #connection: "mysql"
  #table: "tasks"
  #primaryKey: "id"
  #keyType: "int"
  +incrementing: true
  #with: []
  #withCount: []
  +preventsLazyLoading: false
  #perPage: 15
  +exists: true
  +wasRecentlyCreated: false
  #escapeWhenCastingToString: false
  #attributes: array:24 [
    "id" => 1439752
    "created_at" => "2026-04-10 13:58:26"
    "updated_at" => null
    "field_page_start" => "88"
    "field_page_end" => null
    "field_url" => "/9-klass/fizika/izergin-uchebnik/18-2"
    "field_display_title" => "2"
    "field_outside_task" => null
    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037
      #items: array:1 [
        0 => App\Models\Term {#1036
          #connection: "mysql"
          #table: "terms"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: false
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:6 [
            "id" => 26
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "name" => "номер"
            "field_cases" => array:6 [
              "field_accusative_case" => "номер"
              "field_creative_case" => "номером"
              "field_dative_case" => "номеру"
              "field_genitive_case" => "номера"
              "field_nominative_case" => "номер"
              "field_prepositional_case" => "номере"
            ]
            "field_short_name" => "№"
          ]
          #original: array:6 [
            "id" => 26
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "name" => "номер"
            "field_cases" => array:6 [
              "field_accusative_case" => "номер"
              "field_creative_case" => "номером"
              "field_dative_case" => "номеру"
              "field_genitive_case" => "номера"
              "field_nominative_case" => "номер"
              "field_prepositional_case" => "номере"
            ]
            "field_short_name" => "№"
          ]
          #changes: []
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          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
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          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "field_metatags_title" => null
    "field_metatags_description" => null
    "field_h1" => null
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    "field_description_bottom" => null
    "field_match" => null
    "breadcrumbs" => []
    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035
      #items: []
      #escapeWhenCastingToString: false
    }
    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1073
      #items: array:1 [
        0 => App\Models\Branch {#1034
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
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          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 1439560
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Механические колебания и волны"
            "field_branch_order" => "III"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039
              #items: array:1 [
                0 => App\Models\Term {#1038
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
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                  #perPage: 15
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                  #escapeWhenCastingToString: false
                  #attributes: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
                    "field_cases" => array:6 [
                      "field_accusative_case" => "Главу"
                      "field_creative_case" => "Главой"
                      "field_dative_case" => "Главе"
                      "field_genitive_case" => "Главы"
                      "field_nominative_case" => "Глава"
                      "field_prepositional_case" => "Главе"
                    ]
                    "field_page_check_not_needed" => null
                    "field_short_name" => null
                  ]
                  #original: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
                    "field_cases" => array:6 [
                      "field_accusative_case" => "Главу"
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                      "field_genitive_case" => "Главы"
                      "field_nominative_case" => "Глава"
                      "field_prepositional_case" => "Главе"
                    ]
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                    "field_short_name" => null
                  ]
                  #changes: []
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                    0 => "*"
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            "field_page_start" => "67"
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            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
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            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1040
              #items: array:1 [
                0 => App\Models\Book {#1041
                  #connection: "mysql"
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                  #escapeWhenCastingToString: false
                  #attributes: array:50 [
                    "id" => 4169
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_tree_default_status" => "tasks"
                    "field_pages_status" => null
                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1042
                      #items: array:1 [
                        0 => App\Models\Term {#1043
                          #connection: "mysql"
                          #table: "terms"
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                          #keyType: "int"
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                          #attributes: array:10 [ …10]
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                          #changes: []
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                          #dateFormat: null
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                          #hidden: []
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                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1044
                      #items: array:1 [
                        0 => App\Models\Term {#1045
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
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                          #attributes: array:6 [ …6]
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                          #dateFormat: null
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                          +timestamps: true
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                          #hidden: []
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                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046
                      #items: array:1 [
                        0 => App\Models\Term {#1047
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
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                          #attributes: array:6 [ …6]
                          #original: array:6 [ …6]
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                          #dateFormat: null
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                          +timestamps: true
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                          #hidden: []
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                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1048
                      #items: array:1 [
                        0 => App\Models\Term {#1049
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
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                          #attributes: array:12 [ …12]
                          #original: array:12 [ …12]
                          #changes: []
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                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
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                          #touches: []
                          +timestamps: true
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                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1050
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1051
                      #items: array:1 [
                        0 => App\Models\Term {#1052
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
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                          #escapeWhenCastingToString: false
                          #attributes: array:10 [ …10]
                          #original: array:10 [ …10]
                          #changes: []
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                          #dateFormat: null
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                          #visible: []
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                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1053
                      #items: array:1 [
                        0 => App\Models\Term {#1054
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
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                          #attributes: array:6 [ …6]
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                          #touches: []
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                          #hidden: []
                          #visible: []
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                          #guarded: array:1 [ …1]
                        }
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                      #escapeWhenCastingToString: false
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                    "field_city" => Illuminate\Database\Eloquent\Collection {#1055
                      #items: array:1 [
                        0 => App\Models\Term {#1056
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
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                          #visible: []
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                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1057
                      #items: array:1 [
                        0 => App\Models\Term {#1058
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
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                          #attributes: array:8 [ …8]
                          #original: array:8 [ …8]
                          #changes: []
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                        }
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                      #escapeWhenCastingToString: false
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                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1059
                      #items: []
                      #escapeWhenCastingToString: false
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                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1060
                      #items: []
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                    }
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1061
                      #items: array:1 [
                        0 => App\Models\Term {#1062
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
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                    "field_publication_number" => null
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                    "field_cover" => array:1 [
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                    ]
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                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1042}
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                    "field_country" => Illuminate\Database\Eloquent\Collection {#1053}
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1055}
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1057}
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1059}
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1060}
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1061}
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                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064}
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                    "field_allowed" => null
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                    "field_isbn" => "978-5-533-01069-6"
                    "field_cover" => array:1 [
                      0 => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [
                        "path" => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386"
                        "alt" => ""
                        "width" => "1881"
                        "height" => "2502"
                      ]
                    ]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065}
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066}
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067}
                    "field_url" => "/9-klass/fizika/izergin-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 380
                      "subject" => 556
                      "class_subject" => 493
                    ]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070
              #items: []
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1439560
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Механические колебания и волны"
            "field_branch_order" => "III"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039}
            "field_page_start" => "67"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1040}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1108
      #items: array:2 [
        0 => App\Models\Branch {#1116
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 1439560
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Механические колебания и волны"
            "field_branch_order" => "III"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1120
              #items: array:1 [
                0 => App\Models\Term {#1117
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
                    "field_cases" => array:6 [
                      "field_accusative_case" => "Главу"
                      "field_creative_case" => "Главой"
                      "field_dative_case" => "Главе"
                      "field_genitive_case" => "Главы"
                      "field_nominative_case" => "Глава"
                      "field_prepositional_case" => "Главе"
                    ]
                    "field_page_check_not_needed" => null
                    "field_short_name" => null
                  ]
                  #original: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
                    "field_cases" => array:6 [
                      "field_accusative_case" => "Главу"
                      "field_creative_case" => "Главой"
                      "field_dative_case" => "Главе"
                      "field_genitive_case" => "Главы"
                      "field_nominative_case" => "Глава"
                      "field_prepositional_case" => "Главе"
                    ]
                    "field_page_check_not_needed" => null
                    "field_short_name" => null
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "67"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1150
              #items: array:1 [
                0 => App\Models\Book {#1119
                  #connection: "mysql"
                  #table: "books"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:50 [
                    "id" => 4169
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_tree_default_status" => "tasks"
                    "field_pages_status" => null
                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1121
                      #items: array:1 [
                        0 => App\Models\Term {#1118
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6493
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Физика"
                            "field_abbreviated_name" => null
                            "field_cases" => array:6 [
                              "field_accusative_case" => "физику"
                              "field_creative_case" => "физикой"
                              "field_dative_case" => "физике"
                              "field_genitive_case" => "физики"
                              "field_nominative_case" => "физика"
                              "field_prepositional_case" => "физике"
                            ]
                            "field_foreign_lang_name" => null
                            "field_short_name" => null
                            "field_subject_type" => "technical_subject"
                            "field_translit" => "fizika"
                          ]
                          #original: array:10 [
                            "id" => 6493
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Физика"
                            "field_abbreviated_name" => null
                            "field_cases" => array:6 [
                              "field_accusative_case" => "физику"
                              "field_creative_case" => "физикой"
                              "field_dative_case" => "физике"
                              "field_genitive_case" => "физики"
                              "field_nominative_case" => "физика"
                              "field_prepositional_case" => "физике"
                            ]
                            "field_foreign_lang_name" => null
                            "field_short_name" => null
                            "field_subject_type" => "technical_subject"
                            "field_translit" => "fizika"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1122
                      #items: array:1 [
                        0 => App\Models\Term {#1123
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 5458
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "9"
                            "field_cases" => array:6 [
                              "field_accusative_case" => "девятый"
                              "field_creative_case" => "девятым"
                              "field_dative_case" => "девятому"
                              "field_genitive_case" => "девятого"
                              "field_nominative_case" => "девятый"
                              "field_prepositional_case" => "девятом"
                            ]
                            "field_translit" => "devjatyj"
                          ]
                          #original: array:6 [
                            "id" => 5458
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "9"
                            "field_cases" => array:6 [
                              "field_accusative_case" => "девятый"
                              "field_creative_case" => "девятым"
                              "field_dative_case" => "девятому"
                              "field_genitive_case" => "девятого"
                              "field_nominative_case" => "девятый"
                              "field_prepositional_case" => "девятом"
                            ]
                            "field_translit" => "devjatyj"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1124
                      #items: array:1 [
                        0 => App\Models\Term {#1125
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 5176
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Русское слово"
                            "field_cases" => null
                            "field_translit" => "russkoe slovo"
                          ]
                          #original: array:6 [
                            "id" => 5176
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Русское слово"
                            "field_cases" => null
                            "field_translit" => "russkoe slovo"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1126
                      #items: array:1 [
                        0 => App\Models\Term {#1127
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 4491
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Изергин"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Эдуард"
                            "field_patronymic" => "Тимофеевич"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 4491
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Изергин"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Эдуард"
                            "field_patronymic" => "Тимофеевич"
                            "field_surname_rp" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1128
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1129
                      #items: array:1 [
                        0 => App\Models\Term {#1130
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6671
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Учебник"
                            "field_book_type_foreign" => null
                            "field_cases" => array:6 [
                              "field_accusative_case" => "учебник"
                              "field_creative_case" => "учебником"
                              "field_dative_case" => "учебнику"
                              "field_genitive_case" => "учебника"
                              "field_nominative_case" => "учебник"
                              "field_prepositional_case" => "учебнике"
                            ]
                            "field_plural_form" => null
                            "field_short_name" => null
                            "field_short_name_foreign" => null
                            "field_translit" => "uchebnik"
                          ]
                          #original: array:10 [
                            "id" => 6671
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Учебник"
                            "field_book_type_foreign" => null
                            "field_cases" => array:6 [
                              "field_accusative_case" => "учебник"
                              "field_creative_case" => "учебником"
                              "field_dative_case" => "учебнику"
                              "field_genitive_case" => "учебника"
                              "field_nominative_case" => "учебник"
                              "field_prepositional_case" => "учебнике"
                            ]
                            "field_plural_form" => null
                            "field_short_name" => null
                            "field_short_name_foreign" => null
                            "field_translit" => "uchebnik"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1131
                      #items: array:1 [
                        0 => App\Models\Term {#1132
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 9
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Россия"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_translit" => "rossiya"
                          ]
                          #original: array:6 [
                            "id" => 9
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Россия"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_translit" => "rossiya"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1133
                      #items: array:1 [
                        0 => App\Models\Term {#1134
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 15
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Москва"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_translit" => "moskva"
                          ]
                          #original: array:6 [
                            "id" => 15
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Москва"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_translit" => "moskva"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1135
                      #items: array:1 [
                        0 => App\Models\Term {#1136
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:8 [
                            "id" => 4715
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "инновационная школа"
                            "field_cases" => null
                            "field_foreign_lang_series" => null
                            "field_transcription_eng" => null
                            "field_translit" => "innovacionnaya shkola"
                          ]
                          #original: array:8 [
                            "id" => 4715
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "инновационная школа"
                            "field_cases" => null
                            "field_foreign_lang_series" => null
                            "field_transcription_eng" => null
                            "field_translit" => "innovacionnaya shkola"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1137
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1138
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1139
                      #items: array:1 [
                        0 => App\Models\Term {#1140
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6706
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "ФГОС (старый)"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_color" => null
                            "field_end_year" => "2022"
                            "field_start_year" => "2019"
                            "field_translit" => "fgos-old"
                            "field_type" => null
                          ]
                          #original: array:10 [
                            "id" => 6706
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "ФГОС (старый)"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_color" => null
                            "field_end_year" => "2022"
                            "field_start_year" => "2019"
                            "field_translit" => "fgos-old"
                            "field_type" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publication_number" => null
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1141
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1142
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => "2019"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "388"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_09/izergin-u/"
                    "field_isbn" => "978-5-533-01069-6"
                    "field_cover" => array:1 [
                      0 => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [
                        "path" => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386"
                        "alt" => ""
                        "width" => "1881"
                        "height" => "2502"
                      ]
                    ]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1143
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1144
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1145
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_url" => "/9-klass/fizika/izergin-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1146
                      #items: array:1 [
                        0 => App\Models\Term {#1147
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 49
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "синий"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_translit" => "siniy"
                          ]
                          #original: array:6 [
                            "id" => 49
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "синий"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_translit" => "siniy"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 380
                      "subject" => 556
                      "class_subject" => 493
                    ]
                  ]
                  #original: array:50 [
                    "id" => 4169
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_tree_default_status" => "tasks"
                    "field_pages_status" => null
                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1121}
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1122}
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1124}
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1126}
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1128}
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1129}
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1131}
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1133}
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1135}
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1137}
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1138}
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1139}
                    "field_publication_number" => null
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1141}
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1142}
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => "2019"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "388"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_09/izergin-u/"
                    "field_isbn" => "978-5-533-01069-6"
                    "field_cover" => array:1 [
                      0 => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [
                        "path" => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386"
                        "alt" => ""
                        "width" => "1881"
                        "height" => "2502"
                      ]
                    ]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1143}
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1144}
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1145}
                    "field_url" => "/9-klass/fizika/izergin-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1146}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 380
                      "subject" => 556
                      "class_subject" => 493
                    ]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148
              #items: []
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1439560
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Механические колебания и волны"
            "field_branch_order" => "III"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1120}
            "field_page_start" => "67"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1150}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        1 => App\Models\Branch {#1149
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 1439565
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Графическое описание колебательного движения"
            "field_branch_order" => "18"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1154
              #items: array:1 [
                0 => App\Models\Term {#1151
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:7 [
                    "id" => 32
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Параграф"
                    "field_cases" => array:6 [
                      "field_accusative_case" => "Параграф"
                      "field_creative_case" => "Параграфом"
                      "field_dative_case" => "Параграфу"
                      "field_genitive_case" => "Параграфа"
                      "field_nominative_case" => "Параграф"
                      "field_prepositional_case" => "Параграфе"
                    ]
                    "field_page_check_not_needed" => null
                    "field_short_name" => "§"
                  ]
                  #original: array:7 [
                    "id" => 32
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Параграф"
                    "field_cases" => array:6 [
                      "field_accusative_case" => "Параграф"
                      "field_creative_case" => "Параграфом"
                      "field_dative_case" => "Параграфу"
                      "field_genitive_case" => "Параграфа"
                      "field_nominative_case" => "Параграф"
                      "field_prepositional_case" => "Параграфе"
                    ]
                    "field_page_check_not_needed" => null
                    "field_short_name" => "§"
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "85"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1153
              #items: array:1 [
                0 => App\Models\Book {#1119}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1152
              #items: array:1 [
                0 => App\Models\Branch {#1034}
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1439565
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Графическое описание колебательного движения"
            "field_branch_order" => "18"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1154}
            "field_page_start" => "85"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1153}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1152}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "content" => Illuminate\Database\Eloquent\Collection {#1071
      #items: array:2 [
        0 => App\Models\Element {#1099
          #connection: "mysql"
          #table: "elements"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:7 [
            "id" => 1707299
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1091
              #items: array:1 [
                0 => App\Models\Edition {#1098
                  #connection: "mysql"
                  #table: "editions"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:21 [
                    "id" => 6139
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Условие"
                    "field_order" => "1"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1097
                      #items: array:1 [
                        0 => App\Models\Term {#1096
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [ …6]
                          #original: array:6 [ …6]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                           …2
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_content_type" => "free"
                    "field_content_mode" => "text, image"
                    "field_page_content_mode" => "image"
                    "field_content_text_checked" => "0"
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Автор"
                    "field_moderator" => "stas"
                    "field_edition_type" => "statement"
                    "field_root_dir" => "0-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1095
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092
                      #items: []
                      #escapeWhenCastingToString: false
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                    "id" => 6139
                    "created_at" => "2026-04-10 13:58:26"
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                    "field_solution_author" => "Автор"
                    "field_moderator" => "stas"
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                  ]
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            }
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                "path" => "/media/fizika_09/izergin-u/0-18/2-1.webp?ts=1759529230"
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            "created_at" => "2026-04-10 13:58:26"
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            "edition" => Illuminate\Database\Eloquent\Collection {#1091}
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              "type" => "task"
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        1 => App\Models\Element {#1093
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          #attributes: array:6 [
            "id" => 1813317
            "created_at" => "2026-04-10 13:58:26"
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            "edition" => Illuminate\Database\Eloquent\Collection {#1081
              #items: array:1 [
                0 => App\Models\Edition {#1090
                  #connection: "mysql"
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                  #primaryKey: "id"
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                  #attributes: array:21 [
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                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Решение"
                    "field_order" => "2"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1089
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                        0 => App\Models\Term {#1088 …30}
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                    }
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                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1086
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                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1085
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                  ]
                  #original: array:21 [
                    "id" => 6646
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Решение"
                    "field_order" => "2"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1089}
                    "field_content_type" => "free"
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                    "field_solution_author" => "Gemini 2.5 Pro"
                    "field_moderator" => "tolik"
                    "field_edition_type" => "solution"
                    "field_root_dir" => "1-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1086}
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                    "field_content_source" => null
                  ]
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                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "task" => array:2 [
              "refs" => "1439752"
              "type" => "task"
            ]
            "text" => "<p><strong>2.</strong> Какой вид имеет график зависимости смещения колеблющейся точки от времени?</p><p>График зависимости смещения колеблющейся точки от времени, в случае гармонических колебаний, представляет собой синусоиду или косинусоиду.</p><p>Это следует из самого определения гармонических колебаний, которые описываются уравнением вида:<br>$x(t) = A \cdot \cos(\omega t + \phi_0)$<br>или<br>$x(t) = A \cdot \sin(\omega t + \phi_0)$</p><p>Здесь:<br>• $x(t)$ – смещение точки от положения равновесия в момент времени $\text{t}$.<br>• $\text{A}$ – амплитуда колебаний (максимальное смещение от положения равновесия).<br>• $\omega$ – циклическая (угловая) частота.<br>• $\phi_0$ – начальная фаза колебаний, определяющая смещение в начальный момент времени ($t=0$).</p><p>Функции синуса и косинуса являются периодическими, и их графики представляют собой волнообразные кривые. На графике зависимости смещения от времени по оси ординат откладывается смещение $\text{x}$, а по оси абсцисс – время $\text{t}$. Кривая будет колебаться в пределах от $-A$ до $+A$.</p><p><strong>Ответ:</strong> График зависимости смещения колеблющейся точки от времени имеет вид синусоиды (или косинусоиды).</p>"
          ]
          #original: array:6 [
            "id" => 1813317
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1081}
            "task" => array:2 [
              "refs" => "1439752"
              "type" => "task"
            ]
            "text" => "<p><strong>2.</strong> Какой вид имеет график зависимости смещения колеблющейся точки от времени?</p><p>График зависимости смещения колеблющейся точки от времени, в случае гармонических колебаний, представляет собой синусоиду или косинусоиду.</p><p>Это следует из самого определения гармонических колебаний, которые описываются уравнением вида:<br>$x(t) = A \cdot \cos(\omega t + \phi_0)$<br>или<br>$x(t) = A \cdot \sin(\omega t + \phi_0)$</p><p>Здесь:<br>• $x(t)$ – смещение точки от положения равновесия в момент времени $\text{t}$.<br>• $\text{A}$ – амплитуда колебаний (максимальное смещение от положения равновесия).<br>• $\omega$ – циклическая (угловая) частота.<br>• $\phi_0$ – начальная фаза колебаний, определяющая смещение в начальный момент времени ($t=0$).</p><p>Функции синуса и косинуса являются периодическими, и их графики представляют собой волнообразные кривые. На графике зависимости смещения от времени по оси ординат откладывается смещение $\text{x}$, а по оси абсцисс – время $\text{t}$. Кривая будет колебаться в пределах от $-A$ до $+A$.</p><p><strong>Ответ:</strong> График зависимости смещения колеблющейся точки от времени имеет вид синусоиды (или косинусоиды).</p>"
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    "page" => Illuminate\Database\Eloquent\Collection {#1076
      #items: array:1 [
        0 => App\Models\BookPage {#1104
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            "id" => 1439406
            "created_at" => "2026-04-10 13:58:26"
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            }
            "field_weight" => "0"
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                0 => App\Models\Book {#1119}
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            }
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              #items: []
              #escapeWhenCastingToString: false
            }
            "content" => Illuminate\Database\Eloquent\Collection {#1111
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                0 => App\Models\Element {#1115
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                  #primaryKey: "id"
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                  #attributes: array:6 [
                    "id" => 1707644
                    "created_at" => "2026-04-10 13:58:26"
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                    "edition" => Illuminate\Database\Eloquent\Collection {#1109
                      #items: array:1 [
                        0 => App\Models\Edition {#1098}
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                    }
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                        "width" => "1901"
                        "height" => 2557
                        "path" => "/media/fizika_09/izergin-u/0-1/88-1.webp?ts=1759529683"
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                    "id" => 1707644
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "edition" => Illuminate\Database\Eloquent\Collection {#1109}
                    "book_page" => array:2 [
                      "refs" => "1439406"
                      "type" => "book_page"
                    ]
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                      0 => array:5 [
                        "name" => "88-1.jpg"
                        "alt" => null
                        "width" => "1901"
                        "height" => 2557
                        "path" => "/media/fizika_09/izergin-u/0-1/88-1.webp?ts=1759529683"
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                    0 => "*"
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              "refs" => "1439405"
              "type" => "book_page"
            ]
            "tasks" => Illuminate\Database\Eloquent\Collection {#1245
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                0 => App\Models\Task {#1253
                  #connection: "mysql"
                  #table: "tasks"
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                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 1439751
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
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                    "field_display_title" => "1"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1254
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                        0 => App\Models\Term {#1036}
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                    }
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                      #items: []
                      #escapeWhenCastingToString: false
                    }
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                      #items: array:1 [
                        0 => App\Models\Branch {#1116}
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                    }
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1257
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                        0 => App\Models\Branch {#1116}
                        1 => App\Models\Branch {#1149}
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                    "content" => Illuminate\Database\Eloquent\Collection {#1259
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                        1 => App\Models\Element {#1270 …30}
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                    "book" => Illuminate\Database\Eloquent\Collection {#1265
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                        0 => App\Models\Book {#1119}
                      ]
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                    }
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                      "refs" => "1439406"
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                    "book" => Illuminate\Database\Eloquent\Collection {#1265}
                    "page" => array:2 [
                      "refs" => "1439406"
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                    0 => "*"
                  ]
                }
                1 => App\Models\Task {#1260
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                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
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                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 1439752
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "88"
                    "field_page_end" => null
                    "field_url" => "/9-klass/fizika/izergin-uchebnik/18-2"
                    "field_display_title" => "2"
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                        0 => App\Models\Term {#1036}
                      ]
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                    }
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                    }
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                    }
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1261
                      #items: array:2 [
                        0 => App\Models\Branch {#1116}
                        1 => App\Models\Branch {#1149}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "content" => Illuminate\Database\Eloquent\Collection {#1264
                      #items: array:2 [
                        0 => App\Models\Element {#1099}
                        1 => App\Models\Element {#1093}
                      ]
                      #escapeWhenCastingToString: false
                    }
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                        0 => App\Models\Book {#1119}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "page" => array:2 [
                      "refs" => "1439406"
                      "type" => "book_page"
                    ]
                  ]
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                    "id" => 1439752
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                    "updated_at" => null
                    "field_page_start" => "88"
                    "field_page_end" => null
                    "field_url" => "/9-klass/fizika/izergin-uchebnik/18-2"
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№2 (с. 88)

Просмотр Редак-ть Редак-ть (переопр)

Условие. №2 (с. 88)

Редак-ть Редакция

скриншот условия

2. Какой вид имеет график зависимости смещения колеблющейся точки от времени?

Решение. №2 (с. 88)

Редак-ть Редакция

2. Какой вид имеет график зависимости смещения колеблющейся точки от времени?

График зависимости смещения колеблющейся точки от времени, в случае гармонических колебаний, представляет собой синусоиду или косинусоиду.

Это следует из самого определения гармонических колебаний, которые описываются уравнением вида:
$x(t) = A \cdot \cos(\omega t + \phi_0)$
или
$x(t) = A \cdot \sin(\omega t + \phi_0)$

Здесь:
• $x(t)$ – смещение точки от положения равновесия в момент времени $\text{t}$.
• $\text{A}$ – амплитуда колебаний (максимальное смещение от положения равновесия).
• $\omega$ – циклическая (угловая) частота.
• $\phi_0$ – начальная фаза колебаний, определяющая смещение в начальный момент времени ($t=0$).

Функции синуса и косинуса являются периодическими, и их графики представляют собой волнообразные кривые. На графике зависимости смещения от времени по оси ординат откладывается смещение $\text{x}$, а по оси абсцисс – время $\text{t}$. Кривая будет колебаться в пределах от $-A$ до $+A$.

Ответ: График зависимости смещения колеблющейся точки от времени имеет вид синусоиды (или косинусоиды).