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Номер 8, страница 51, часть 2 - гдз по физике 9 класс рабочая тетрадь Грачев, Погожев
Авторы: Грачев А. В., Погожев В. А., Боков П. Ю., Вишнякова Е. А.
Тип: рабочая тетрадь
Издательство: Просвещение
Год издания: 2021 - 2026
Часть: 2
Цвет обложки: синий
ISBN: 978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)
Популярные ГДЗ в 9 классе
Часть 2. Глава 6. Механические колебания и волны. Параграф 31. Механические колебания - номер 8, страница 51.
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" => 1435135 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "51" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/31-8" "field_display_title" => "8" "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: [] #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 "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ 0 => App\Models\Branch {#1034 #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" => 1434829 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "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: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #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" => "3" "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 #items: array:1 [ 0 => App\Models\Book {#1041 #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" => 1203 "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 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1044 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1048 #items: array:4 [ …4] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1053 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1058 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ …4] 1 => array:4 [ …4] …1 ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 1203 "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} "field_class" => Illuminate\Database\Eloquent\Collection {#1044} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046} "field_author" => Illuminate\Database\Eloquent\Collection {#1048} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1053} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1054} "field_country" => Illuminate\Database\Eloquent\Collection {#1056} "field_city" => Illuminate\Database\Eloquent\Collection {#1058} "field_series" => Illuminate\Database\Eloquent\Collection {#1060} "field_umk" => Illuminate\Database\Eloquent\Collection {#1061} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1062} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ …3] "field_cover_alts" => array:3 [ …3] "field_covers" => array:3 [ …3] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1073 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434829 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "3" "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 {#1073} ] #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 {#1160 #items: array:3 [ 0 => App\Models\Branch {#1170 #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" => 1434829 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1174 #items: array:1 [ 0 => App\Models\Term {#1171 #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" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #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" => "3" "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 {#1207 #items: array:1 [ 0 => App\Models\Book {#1173 #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" => 1203 "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 {#1175 #items: array:1 [ 0 => App\Models\Term {#1172 #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 [ …6] "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 [ …6] "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 {#1176 #items: array:1 [ 0 => App\Models\Term {#1177 #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 [ …6] "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 [ …6] "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 {#1178 #items: array:1 [ 0 => App\Models\Term {#1179 #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" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #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 {#1180 #items: array:4 [ 0 => App\Models\Term {#1181 #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" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "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 => "*" ] } 1 => App\Models\Term {#1182 #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" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Александрович" "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 => "*" ] } 2 => App\Models\Term {#1183 #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" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "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 => "*" ] } 3 => App\Models\Term {#1184 #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" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "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 {#1185 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1186 #items: array:1 [ 0 => App\Models\Term {#1187 #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" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #original: array:10 [ "id" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #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 {#1188 #items: array:1 [ 0 => App\Models\Term {#1189 #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 [ …6] "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 [ …6] "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 {#1190 #items: array:1 [ 0 => App\Models\Term {#1191 #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 [ …6] "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 [ …6] "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 {#1192 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1193 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1194 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1195 #items: array:1 [ 0 => App\Models\Term {#1196 #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 [ …6] "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 [ …6] "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" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1197 #items: array:1 [ 0 => App\Models\Term {#1198 #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" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ …6] "field_translit" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ …6] "field_translit" => "stereotipnoe" ] #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_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1199 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1200 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1201 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1202 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1203 #items: array:1 [ 0 => App\Models\Term {#1204 #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 [ …6] "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 [ …6] "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" => 1203 "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 {#1175} "field_class" => Illuminate\Database\Eloquent\Collection {#1176} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1178} "field_author" => Illuminate\Database\Eloquent\Collection {#1180} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1185} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1186} "field_country" => Illuminate\Database\Eloquent\Collection {#1188} "field_city" => Illuminate\Database\Eloquent\Collection {#1190} "field_series" => Illuminate\Database\Eloquent\Collection {#1192} "field_umk" => Illuminate\Database\Eloquent\Collection {#1193} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1194} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1195} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1197} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1199} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1200} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1201} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1202} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1203} "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 {#1205 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434829 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1174} "field_page_start" => "3" "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 {#1207} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1205} ] #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 {#1206 #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" => 1434841 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические колебания и волны" "field_branch_order" => "6" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1211 #items: array:1 [ 0 => App\Models\Term {#1208 #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 [ …6] "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 [ …6] "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" => "48" "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 {#1210 #items: array:1 [ 0 => App\Models\Book {#1173} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1209 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434841 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические колебания и волны" "field_branch_order" => "6" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1211} "field_page_start" => "48" "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 {#1210} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1209} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Branch {#1212 #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" => 1434842 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические колебания" "field_branch_order" => "31" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1216 #items: array:1 [ 0 => App\Models\Term {#1213 #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 [ …6] "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 [ …6] "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" => "48" "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 {#1215 #items: array:1 [ 0 => App\Models\Book {#1173} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1224 #items: array:1 [ 0 => App\Models\Branch {#1223 #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" => 1434841 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические колебания и волны" "field_branch_order" => "6" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1225 …2} "field_page_start" => "48" "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 {#1226 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1227 …2} ] #original: array:24 [ "id" => 1434841 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические колебания и волны" "field_branch_order" => "6" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1225 …2} "field_page_start" => "48" "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 {#1226 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1227 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434842 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические колебания" "field_branch_order" => "31" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1216} "field_page_start" => "48" "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 {#1215} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1224} ] #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 {#1112 #items: array:2 [ 0 => App\Models\Element {#1147 #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" => 1698523 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1137 #items: array:1 [ 0 => App\Models\Edition {#1145 #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" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1143 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "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 {#1142 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1143 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "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 {#1142 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_content_source" => 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 } "task" => array:2 [ "refs" => "1435135" "type" => "task" ] "text" => "<p><strong>8.</strong> На рис. 26 показан график движения груза пружинного маятника, совершающего гармонические колебания. Используя этот график, выполните следующие задания.</p><p><strong>а)</strong> Определите:</p><p>амплитуду колебаний $A = $ ________</p><p>период колебаний $T = $ ________</p><p>частоту колебаний $v = $ ________</p><p><strong>б)</strong> Найдите:</p><p>модули перемещений груза за первые 0,4 с ($\vert \Delta x_{0,4} \vert$) и за первые 0,6 с ($\vert \Delta x_{0,6} \vert$).</p><p>$\vert \Delta x_{0,4} \vert = $ ________ $\vert \Delta x_{0,6} \vert = $ ________</p><p>пути, пройденные грузом, за первые 0,4 с ($\Delta s_{0,4}$) и за первые 0,6 с ($\Delta s_{0,6}$).</p><p>$\Delta s_{0,4} = $ ________ $\Delta s_{0,6} = $ ________</p><p><strong>в)</strong> Считая, что приведённый график является графиком движения груза пружинного маятника, изображённого на рис. 123 учебника, определите моменты времени, соответствующие положениям б, в, г, д, е на рис. 123:</p><p>$t_б = $ ________ $t_в = $ ________ $t_г = $ ________ $t_д = $ ________ $t_e = $ ________</p><p><strong>г) Укажите промежутки времени, когда груз движется в положительном направлении оси $\text{X}$</strong> ________ , когда груз движется<br>в отрицательном направлении оси $\text{X}$ ________</p><p><strong>д) Укажите моменты времени, когда модуль скорости груза максимален</strong> ________<br>, когда модуль скорости груза минимален ________</p>" "img" => array:1 [ 0 => array:5 [ "name" => "8-1.jpg" "alt" => null "width" => "1980" "height" => 1708 "path" => "/media/fizika_09/grachev-rt/0-31/8-1.webp?ts=1759402778" ] ] ] #original: array:7 [ "id" => 1698523 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1137} "task" => array:2 [ "refs" => "1435135" "type" => "task" ] "text" => "<p><strong>8.</strong> На рис. 26 показан график движения груза пружинного маятника, совершающего гармонические колебания. Используя этот график, выполните следующие задания.</p><p><strong>а)</strong> Определите:</p><p>амплитуду колебаний $A = $ ________</p><p>период колебаний $T = $ ________</p><p>частоту колебаний $v = $ ________</p><p><strong>б)</strong> Найдите:</p><p>модули перемещений груза за первые 0,4 с ($\vert \Delta x_{0,4} \vert$) и за первые 0,6 с ($\vert \Delta x_{0,6} \vert$).</p><p>$\vert \Delta x_{0,4} \vert = $ ________ $\vert \Delta x_{0,6} \vert = $ ________</p><p>пути, пройденные грузом, за первые 0,4 с ($\Delta s_{0,4}$) и за первые 0,6 с ($\Delta s_{0,6}$).</p><p>$\Delta s_{0,4} = $ ________ $\Delta s_{0,6} = $ ________</p><p><strong>в)</strong> Считая, что приведённый график является графиком движения груза пружинного маятника, изображённого на рис. 123 учебника, определите моменты времени, соответствующие положениям б, в, г, д, е на рис. 123:</p><p>$t_б = $ ________ $t_в = $ ________ $t_г = $ ________ $t_д = $ ________ $t_e = $ ________</p><p><strong>г) Укажите промежутки времени, когда груз движется в положительном направлении оси $\text{X}$</strong> ________ , когда груз движется<br>в отрицательном направлении оси $\text{X}$ ________</p><p><strong>д) Укажите моменты времени, когда модуль скорости груза максимален</strong> ________<br>, когда модуль скорости груза минимален ________</p>" "img" => array:1 [ 0 => array:5 [ "name" => "8-1.jpg" "alt" => null "width" => "1980" "height" => 1708 "path" => "/media/fizika_09/grachev-rt/0-31/8-1.webp?ts=1759402778" ] ] ] #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\Element {#1138 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1734509 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Edition {#1139 #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" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_content_source" => 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 } "task" => array:2 [ "refs" => "1435135" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>График зависимости координаты груза от времени $x(t)$.</p><p><strong>Найти:</strong></p><p>а) Амплитуду $A$, период $T$, частоту $v$.</p><p>б) Модули перемещений $|\Delta x_{0,4}|$, $|\Delta x_{0,6}|$ и пути $\Delta s_{0,4}$, $\Delta s_{0,6}$.</p><p>в) Моменты времени $t_б, t_в, t_г, t_д, t_е$.</p><p>г) Промежутки времени движения в положительном и отрицательном направлениях оси Х.</p><p>д) Моменты времени, когда модуль скорости максимален и минимален.</p><p><strong>Решение:</strong></p><p><strong>а) Определите:</strong></p><p>Амплитуда колебаний $A$ — это максимальное отклонение тела от положения равновесия. По графику максимальное значение координаты $x_{max} = 0,2$ м, следовательно, амплитуда $A = 0,2$ м.</p><p>Период колебаний $T$ — это время, за которое совершается одно полное колебание. Из графика видно, что движение повторяется через каждые 0,4 с (например, тело проходит положение равновесия в одном и том же направлении в моменты времени $t = 0$ с, $t = 0,4$ с, $t = 0,8$ с). Таким образом, период $T = 0,4$ с.</p><p>Частота колебаний $v$ — это величина, обратная периоду: $v = 1/T$.</p><p>$v = \frac{1}{0,4 \text{ с}} = 2,5$ Гц.</p><p><strong>Ответ:</strong> амплитуда колебаний $A = 0,2$ м, период колебаний $T = 0,4$ с, частота колебаний $v = 2,5$ Гц.</p><p><strong>б) Найдите:</strong></p><p>Модуль перемещения $|\Delta x|$ определяется как модуль разности конечной и начальной координат $|\Delta x| = |x_{кон} - x_{нач}|$.</p><p>За первые 0,4 с: начальная координата $x(0) = 0$ м, конечная координата $x(0,4) = 0$ м. Модуль перемещения $|\Delta x_{0,4}| = |0 - 0| = 0$ м.</p><p>За первые 0,6 с: начальная координата $x(0) = 0$ м, конечная координата $x(0,6) = 0$ м. Модуль перемещения $|\Delta x_{0,6}| = |0 - 0| = 0$ м.</p><p>Путь $\Delta s$ — это расстояние, пройденное телом вдоль траектории.</p><p>За первые 0,4 с (один полный период) груз проходит расстояние, равное четырем амплитудам: $\Delta s_{0,4} = 4A = 4 \cdot 0,2 \text{ м} = 0,8$ м.</p><p>За первые 0,6 с (полтора периода) груз проходит расстояние, равное шести амплитудам: $\Delta s_{0,6} = 1,5 \cdot (4A) = 6A = 6 \cdot 0,2 \text{ м} = 1,2$ м.</p><p><strong>Ответ:</strong> $|\Delta x_{0,4}| = 0$ м, $|\Delta x_{0,6}| = 0$ м, $\Delta s_{0,4} = 0,8$ м, $\Delta s_{0,6} = 1,2$ м.</p><p><strong>в) Считая, что приведённый график является графиком движения груза пружинного маятника, изображённого на рис. 123 учебника, определите моменты времени, соответствующие положениям б, в, г, д, е на рис. 123:</strong></p><p>Так как изображение с рис. 123 отсутствует, будем считать, что указанные положения соответствуют ключевым точкам одного цикла колебаний:</p><ul> <li>$t_б$ — момент времени, когда тело находится в положении максимального положительного отклонения ($x = +A$). Из графика $t_б = 0,1$ с.</li> <li>$t_в$ — момент времени, когда тело проходит положение равновесия ($x = 0$), двигаясь в отрицательном направлении. Из графика $t_в = 0,2$ с.</li> <li>$t_г$ — момент времени, когда тело находится в положении максимального отрицательного отклонения ($x = -A$). Из графика $t_г = 0,3$ с.</li> <li>$t_д$ — момент времени, когда тело проходит положение равновесия ($x = 0$), двигаясь в положительном направлении. Из графика $t_д = 0,4$ с.</li> <li>$t_е$ — момент времени, когда тело снова достигает максимального положительного отклонения ($x = +A$). Из графика $t_е = 0,5$ с.</li></ul><p><strong>Ответ:</strong> $t_б = 0,1$ с, $t_в = 0,2$ с, $t_г = 0,3$ с, $t_д = 0,4$ с, $t_е = 0,5$ с.</p><p><strong>г) Укажите промежутки времени, когда груз движется в положительном направлении оси Х, когда груз движется в отрицательном направлении оси Х:</strong></p><p>Груз движется в положительном направлении оси X, когда его координата $x$ увеличивается (график идет вверх). Это происходит на временных интервалах: $(0; 0,1)$ с, $(0,3; 0,5)$ с, $(0,7; 0,9)$ с и т.д.</p><p>Груз движется в отрицательном направлении оси X, когда его координата $x$ уменьшается (график идет вниз). Это происходит на временных интервалах: $(0,1; 0,3)$ с, $(0,5; 0,7)$ с и т.д.</p><p><strong>Ответ:</strong> груз движется в положительном направлении оси X в промежутки времени $(0,4k-0,1; 0,4k+0,1)$ с для $k \geq 1$ и $(0; 0,1)$ с. Груз движется в отрицательном направлении оси X в промежутки времени $(0,1+0,4k; 0,3+0,4k)$ с, где $k=0, 1, 2, ...$</p><p><strong>д) Укажите моменты времени, когда модуль скорости груза максимален, когда модуль скорости груза минимален:</strong></p><p>Модуль скорости груза максимален в моменты прохождения положения равновесия ($x=0$), где наклон графика максимален по модулю. По графику это происходит в моменты времени $t = 0$ с, $0,2$ с, $0,4$ с, $0,6$ с, $0,8$ с и т.д. В общем виде: $t = k \cdot \frac{T}{2} = 0,2k$ с, где $k=0, 1, 2, ...$</p><p>Модуль скорости груза минимален (равен нулю) в моменты достижения крайних положений ($x = \pm A$), где наклон графика равен нулю. По графику это происходит в моменты времени $t = 0,1$ с, $0,3$ с, $0,5$ с, $0,7$ с и т.д. В общем виде: $t = \frac{T}{4} + k \cdot \frac{T}{2} = 0,1 + 0,2k$ с, где $k=0, 1, 2, ...$</p><p><strong>Ответ:</strong> модуль скорости максимален в моменты времени $t = 0,2k$ с; модуль скорости минимален в моменты времени $t = 0,1 + 0,2k$ с, где $k$ – целое неотрицательное число ($k=0, 1, 2, ...$).</p>" ] #original: array:6 [ "id" => 1734509 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1130} "task" => array:2 [ "refs" => "1435135" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>График зависимости координаты груза от времени $x(t)$.</p><p><strong>Найти:</strong></p><p>а) Амплитуду $A$, период $T$, частоту $v$.</p><p>б) Модули перемещений $|\Delta x_{0,4}|$, $|\Delta x_{0,6}|$ и пути $\Delta s_{0,4}$, $\Delta s_{0,6}$.</p><p>в) Моменты времени $t_б, t_в, t_г, t_д, t_е$.</p><p>г) Промежутки времени движения в положительном и отрицательном направлениях оси Х.</p><p>д) Моменты времени, когда модуль скорости максимален и минимален.</p><p><strong>Решение:</strong></p><p><strong>а) Определите:</strong></p><p>Амплитуда колебаний $A$ — это максимальное отклонение тела от положения равновесия. По графику максимальное значение координаты $x_{max} = 0,2$ м, следовательно, амплитуда $A = 0,2$ м.</p><p>Период колебаний $T$ — это время, за которое совершается одно полное колебание. Из графика видно, что движение повторяется через каждые 0,4 с (например, тело проходит положение равновесия в одном и том же направлении в моменты времени $t = 0$ с, $t = 0,4$ с, $t = 0,8$ с). Таким образом, период $T = 0,4$ с.</p><p>Частота колебаний $v$ — это величина, обратная периоду: $v = 1/T$.</p><p>$v = \frac{1}{0,4 \text{ с}} = 2,5$ Гц.</p><p><strong>Ответ:</strong> амплитуда колебаний $A = 0,2$ м, период колебаний $T = 0,4$ с, частота колебаний $v = 2,5$ Гц.</p><p><strong>б) Найдите:</strong></p><p>Модуль перемещения $|\Delta x|$ определяется как модуль разности конечной и начальной координат $|\Delta x| = |x_{кон} - x_{нач}|$.</p><p>За первые 0,4 с: начальная координата $x(0) = 0$ м, конечная координата $x(0,4) = 0$ м. Модуль перемещения $|\Delta x_{0,4}| = |0 - 0| = 0$ м.</p><p>За первые 0,6 с: начальная координата $x(0) = 0$ м, конечная координата $x(0,6) = 0$ м. Модуль перемещения $|\Delta x_{0,6}| = |0 - 0| = 0$ м.</p><p>Путь $\Delta s$ — это расстояние, пройденное телом вдоль траектории.</p><p>За первые 0,4 с (один полный период) груз проходит расстояние, равное четырем амплитудам: $\Delta s_{0,4} = 4A = 4 \cdot 0,2 \text{ м} = 0,8$ м.</p><p>За первые 0,6 с (полтора периода) груз проходит расстояние, равное шести амплитудам: $\Delta s_{0,6} = 1,5 \cdot (4A) = 6A = 6 \cdot 0,2 \text{ м} = 1,2$ м.</p><p><strong>Ответ:</strong> $|\Delta x_{0,4}| = 0$ м, $|\Delta x_{0,6}| = 0$ м, $\Delta s_{0,4} = 0,8$ м, $\Delta s_{0,6} = 1,2$ м.</p><p><strong>в) Считая, что приведённый график является графиком движения груза пружинного маятника, изображённого на рис. 123 учебника, определите моменты времени, соответствующие положениям б, в, г, д, е на рис. 123:</strong></p><p>Так как изображение с рис. 123 отсутствует, будем считать, что указанные положения соответствуют ключевым точкам одного цикла колебаний:</p><ul> <li>$t_б$ — момент времени, когда тело находится в положении максимального положительного отклонения ($x = +A$). Из графика $t_б = 0,1$ с.</li> <li>$t_в$ — момент времени, когда тело проходит положение равновесия ($x = 0$), двигаясь в отрицательном направлении. Из графика $t_в = 0,2$ с.</li> <li>$t_г$ — момент времени, когда тело находится в положении максимального отрицательного отклонения ($x = -A$). Из графика $t_г = 0,3$ с.</li> <li>$t_д$ — момент времени, когда тело проходит положение равновесия ($x = 0$), двигаясь в положительном направлении. Из графика $t_д = 0,4$ с.</li> <li>$t_е$ — момент времени, когда тело снова достигает максимального положительного отклонения ($x = +A$). Из графика $t_е = 0,5$ с.</li></ul><p><strong>Ответ:</strong> $t_б = 0,1$ с, $t_в = 0,2$ с, $t_г = 0,3$ с, $t_д = 0,4$ с, $t_е = 0,5$ с.</p><p><strong>г) Укажите промежутки времени, когда груз движется в положительном направлении оси Х, когда груз движется в отрицательном направлении оси Х:</strong></p><p>Груз движется в положительном направлении оси X, когда его координата $x$ увеличивается (график идет вверх). Это происходит на временных интервалах: $(0; 0,1)$ с, $(0,3; 0,5)$ с, $(0,7; 0,9)$ с и т.д.</p><p>Груз движется в отрицательном направлении оси X, когда его координата $x$ уменьшается (график идет вниз). Это происходит на временных интервалах: $(0,1; 0,3)$ с, $(0,5; 0,7)$ с и т.д.</p><p><strong>Ответ:</strong> груз движется в положительном направлении оси X в промежутки времени $(0,4k-0,1; 0,4k+0,1)$ с для $k \geq 1$ и $(0; 0,1)$ с. Груз движется в отрицательном направлении оси X в промежутки времени $(0,1+0,4k; 0,3+0,4k)$ с, где $k=0, 1, 2, ...$</p><p><strong>д) Укажите моменты времени, когда модуль скорости груза максимален, когда модуль скорости груза минимален:</strong></p><p>Модуль скорости груза максимален в моменты прохождения положения равновесия ($x=0$), где наклон графика максимален по модулю. По графику это происходит в моменты времени $t = 0$ с, $0,2$ с, $0,4$ с, $0,6$ с, $0,8$ с и т.д. В общем виде: $t = k \cdot \frac{T}{2} = 0,2k$ с, где $k=0, 1, 2, ...$</p><p>Модуль скорости груза минимален (равен нулю) в моменты достижения крайних положений ($x = \pm A$), где наклон графика равен нулю. По графику это происходит в моменты времени $t = 0,1$ с, $0,3$ с, $0,5$ с, $0,7$ с и т.д. В общем виде: $t = \frac{T}{4} + k \cdot \frac{T}{2} = 0,1 + 0,2k$ с, где $k=0, 1, 2, ...$</p><p><strong>Ответ:</strong> модуль скорости максимален в моменты времени $t = 0,2k$ с; модуль скорости минимален в моменты времени $t = 0,1 + 0,2k$ с, где $k$ – целое неотрицательное число ($k=0, 1, 2, ...$).</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1435136" "type" => "task" ] "previous" => array:2 [ "refs" => "1435134" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1157 #items: array:1 [ 0 => App\Models\Book {#1173} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\BookPage {#1158 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Illuminate\Database\Eloquent\Collection {#1099 #items: array:1 [ 0 => App\Models\Book {#1173} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1098 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1088 #items: array:1 [ 0 => App\Models\Element {#1089 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1699073 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1087 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1699073 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1087 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1435687" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1435685" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1097 #items: array:3 [ 0 => App\Models\Task {#1080 #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" => 1435323 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№8 (с. 51)
Условие. №8 (с. 51)
скриншот условия
8. На рис. 26 показан график движения груза пружинного маятника, совершающего гармонические колебания. Используя этот график, выполните следующие задания.
а) Определите:
амплитуду колебаний $A = $ ________
период колебаний $T = $ ________
частоту колебаний $v = $ ________
б) Найдите:
модули перемещений груза за первые 0,4 с ($\vert \Delta x_{0,4} \vert$) и за первые 0,6 с ($\vert \Delta x_{0,6} \vert$).
$\vert \Delta x_{0,4} \vert = $ ________ $\vert \Delta x_{0,6} \vert = $ ________
пути, пройденные грузом, за первые 0,4 с ($\Delta s_{0,4}$) и за первые 0,6 с ($\Delta s_{0,6}$).
$\Delta s_{0,4} = $ ________ $\Delta s_{0,6} = $ ________
в) Считая, что приведённый график является графиком движения груза пружинного маятника, изображённого на рис. 123 учебника, определите моменты времени, соответствующие положениям б, в, г, д, е на рис. 123:
$t_б = $ ________ $t_в = $ ________ $t_г = $ ________ $t_д = $ ________ $t_e = $ ________
г) Укажите промежутки времени, когда груз движется в положительном направлении оси $\text{X}$ ________ , когда груз движется
в отрицательном направлении оси $\text{X}$ ________
д) Укажите моменты времени, когда модуль скорости груза максимален ________
, когда модуль скорости груза минимален ________
Решение. №8 (с. 51)
Дано:
График зависимости координаты груза от времени $x(t)$.
Найти:
а) Амплитуду $A$, период $T$, частоту $v$.
б) Модули перемещений $|\Delta x_{0,4}|$, $|\Delta x_{0,6}|$ и пути $\Delta s_{0,4}$, $\Delta s_{0,6}$.
в) Моменты времени $t_б, t_в, t_г, t_д, t_е$.
г) Промежутки времени движения в положительном и отрицательном направлениях оси Х.
д) Моменты времени, когда модуль скорости максимален и минимален.
Решение:
а) Определите:
Амплитуда колебаний $A$ — это максимальное отклонение тела от положения равновесия. По графику максимальное значение координаты $x_{max} = 0,2$ м, следовательно, амплитуда $A = 0,2$ м.
Период колебаний $T$ — это время, за которое совершается одно полное колебание. Из графика видно, что движение повторяется через каждые 0,4 с (например, тело проходит положение равновесия в одном и том же направлении в моменты времени $t = 0$ с, $t = 0,4$ с, $t = 0,8$ с). Таким образом, период $T = 0,4$ с.
Частота колебаний $v$ — это величина, обратная периоду: $v = 1/T$.
$v = \frac{1}{0,4 \text{ с}} = 2,5$ Гц.
Ответ: амплитуда колебаний $A = 0,2$ м, период колебаний $T = 0,4$ с, частота колебаний $v = 2,5$ Гц.
б) Найдите:
Модуль перемещения $|\Delta x|$ определяется как модуль разности конечной и начальной координат $|\Delta x| = |x_{кон} - x_{нач}|$.
За первые 0,4 с: начальная координата $x(0) = 0$ м, конечная координата $x(0,4) = 0$ м. Модуль перемещения $|\Delta x_{0,4}| = |0 - 0| = 0$ м.
За первые 0,6 с: начальная координата $x(0) = 0$ м, конечная координата $x(0,6) = 0$ м. Модуль перемещения $|\Delta x_{0,6}| = |0 - 0| = 0$ м.
Путь $\Delta s$ — это расстояние, пройденное телом вдоль траектории.
За первые 0,4 с (один полный период) груз проходит расстояние, равное четырем амплитудам: $\Delta s_{0,4} = 4A = 4 \cdot 0,2 \text{ м} = 0,8$ м.
За первые 0,6 с (полтора периода) груз проходит расстояние, равное шести амплитудам: $\Delta s_{0,6} = 1,5 \cdot (4A) = 6A = 6 \cdot 0,2 \text{ м} = 1,2$ м.
Ответ: $|\Delta x_{0,4}| = 0$ м, $|\Delta x_{0,6}| = 0$ м, $\Delta s_{0,4} = 0,8$ м, $\Delta s_{0,6} = 1,2$ м.
в) Считая, что приведённый график является графиком движения груза пружинного маятника, изображённого на рис. 123 учебника, определите моменты времени, соответствующие положениям б, в, г, д, е на рис. 123:
Так как изображение с рис. 123 отсутствует, будем считать, что указанные положения соответствуют ключевым точкам одного цикла колебаний:
- $t_б$ — момент времени, когда тело находится в положении максимального положительного отклонения ($x = +A$). Из графика $t_б = 0,1$ с.
- $t_в$ — момент времени, когда тело проходит положение равновесия ($x = 0$), двигаясь в отрицательном направлении. Из графика $t_в = 0,2$ с.
- $t_г$ — момент времени, когда тело находится в положении максимального отрицательного отклонения ($x = -A$). Из графика $t_г = 0,3$ с.
- $t_д$ — момент времени, когда тело проходит положение равновесия ($x = 0$), двигаясь в положительном направлении. Из графика $t_д = 0,4$ с.
- $t_е$ — момент времени, когда тело снова достигает максимального положительного отклонения ($x = +A$). Из графика $t_е = 0,5$ с.
Ответ: $t_б = 0,1$ с, $t_в = 0,2$ с, $t_г = 0,3$ с, $t_д = 0,4$ с, $t_е = 0,5$ с.
г) Укажите промежутки времени, когда груз движется в положительном направлении оси Х, когда груз движется в отрицательном направлении оси Х:
Груз движется в положительном направлении оси X, когда его координата $x$ увеличивается (график идет вверх). Это происходит на временных интервалах: $(0; 0,1)$ с, $(0,3; 0,5)$ с, $(0,7; 0,9)$ с и т.д.
Груз движется в отрицательном направлении оси X, когда его координата $x$ уменьшается (график идет вниз). Это происходит на временных интервалах: $(0,1; 0,3)$ с, $(0,5; 0,7)$ с и т.д.
Ответ: груз движется в положительном направлении оси X в промежутки времени $(0,4k-0,1; 0,4k+0,1)$ с для $k \geq 1$ и $(0; 0,1)$ с. Груз движется в отрицательном направлении оси X в промежутки времени $(0,1+0,4k; 0,3+0,4k)$ с, где $k=0, 1, 2, ...$
д) Укажите моменты времени, когда модуль скорости груза максимален, когда модуль скорости груза минимален:
Модуль скорости груза максимален в моменты прохождения положения равновесия ($x=0$), где наклон графика максимален по модулю. По графику это происходит в моменты времени $t = 0$ с, $0,2$ с, $0,4$ с, $0,6$ с, $0,8$ с и т.д. В общем виде: $t = k \cdot \frac{T}{2} = 0,2k$ с, где $k=0, 1, 2, ...$
Модуль скорости груза минимален (равен нулю) в моменты достижения крайних положений ($x = \pm A$), где наклон графика равен нулю. По графику это происходит в моменты времени $t = 0,1$ с, $0,3$ с, $0,5$ с, $0,7$ с и т.д. В общем виде: $t = \frac{T}{4} + k \cdot \frac{T}{2} = 0,1 + 0,2k$ с, где $k=0, 1, 2, ...$
Ответ: модуль скорости максимален в моменты времени $t = 0,2k$ с; модуль скорости минимален в моменты времени $t = 0,1 + 0,2k$ с, где $k$ – целое неотрицательное число ($k=0, 1, 2, ...$).
Другие задания:
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