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Номер 3, страница 185 - гдз по физике 9 класс учебник Шахмаев, Бунчук
Авторы: Шахмаев Н. М., Бунчук А. В.
Тип: Учебник
Издательство: Мнемозина
Год издания: 2007 - 2026
Цвет обложки: голубой
ISBN: 978-5-346-01799-8
Популярные ГДЗ в 9 классе
Глава 10. Механические колебания и волны. Параграф 39. График колебаний - номер 3, страница 185.
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" => 1437132 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "185" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/39-3" "field_display_title" => "3" "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 {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #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" => 1436838 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические колебания и волны" "field_branch_order" => "10" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1047 #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" => "178" "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 {#1080 #items: array:1 [ 0 => App\Models\Book {#1049 #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" => 2906 "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 {#1051 #items: array:1 [ 0 => App\Models\Term {#1048 #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 {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #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 {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #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" => 5155 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Мнемозина" "field_cases" => null "field_translit" => "mnemozina" ] #original: array:6 [ "id" => 5155 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Мнемозина" "field_cases" => null "field_translit" => "mnemozina" ] #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 {#1056 #items: array:2 [ 0 => App\Models\Term {#1057 #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" => 6294 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Шахмаев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Николай" "field_patronymic" => "Михайлович" "field_surname_rp" => null ] #original: array:12 [ "id" => 6294 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Шахмаев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Николай" "field_patronymic" => "Михайлович" "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 {#1058 #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" => 3942 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бунчук" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алексей" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 3942 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бунчук" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алексей" "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 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ 0 => App\Models\Term {#1061 #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 {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 #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 {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #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 {#1066 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "4" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1070 #items: array:1 [ 0 => App\Models\Term {#1071 #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 [ "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" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "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" => "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 {#1072 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2007" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "362" "field_priority" => null "field_default_folder" => "/fizika_09/shahmaev-u/" "field_isbn" => "978-5-346-01799-8" "field_cover" => array:1 [ 0 => "/media/fizika_09/shahmaev-u/covers/cover1.webp?ts=1759080267" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/shahmaev-u/covers/cover1.webp?ts=1759080267" "alt" => "" "width" => "2294" "height" => "3039" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/shahmaev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ 0 => App\Models\Term {#1077 #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" => 52 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "голубой" "field_cases" => array:6 [ "field_accusative_case" => "голубой" "field_creative_case" => "голубым" "field_dative_case" => "голубому" "field_genitive_case" => "голубого" "field_nominative_case" => "голубой" "field_prepositional_case" => "голубом" ] "field_translit" => "goluboy" ] #original: array:6 [ "id" => 52 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "голубой" "field_cases" => array:6 [ "field_accusative_case" => "голубой" "field_creative_case" => "голубым" "field_dative_case" => "голубому" "field_genitive_case" => "голубого" "field_nominative_case" => "голубой" "field_prepositional_case" => "голубом" ] "field_translit" => "goluboy" ] #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" => 2906 "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 {#1051} "field_class" => Illuminate\Database\Eloquent\Collection {#1052} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054} "field_author" => Illuminate\Database\Eloquent\Collection {#1056} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1059} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1060} "field_country" => Illuminate\Database\Eloquent\Collection {#1062} "field_city" => Illuminate\Database\Eloquent\Collection {#1064} "field_series" => Illuminate\Database\Eloquent\Collection {#1066} "field_umk" => Illuminate\Database\Eloquent\Collection {#1067} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1068} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1069} "field_publication_number" => "4" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1070} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1072} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2007" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "362" "field_priority" => null "field_default_folder" => "/fizika_09/shahmaev-u/" "field_isbn" => "978-5-346-01799-8" "field_cover" => array:1 [ 0 => "/media/fizika_09/shahmaev-u/covers/cover1.webp?ts=1759080267" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/shahmaev-u/covers/cover1.webp?ts=1759080267" "alt" => "" "width" => "2294" "height" => "3039" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1073} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1074} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1075} "field_url" => "/9-klass/fizika/shahmaev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1076} "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 {#1078 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1436838 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические колебания и волны" "field_branch_order" => "10" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_page_start" => "178" "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 {#1080} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1078} ] #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 {#1109 #items: array:2 [ 0 => App\Models\Branch {#1117 #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" => 1436838 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические колебания и волны" "field_branch_order" => "10" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1118 #items: array:1 [ 0 => App\Models\Term {#1047} ] #escapeWhenCastingToString: false } "field_page_start" => "178" "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 {#1119 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1120 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1436838 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические колебания и волны" "field_branch_order" => "10" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1118} "field_page_start" => "178" "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 {#1119} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1120} ] #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 {#1121 #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" => 1436840 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "График колебаний" "field_branch_order" => "39" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\Term {#1122 #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" => "182" "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 {#1124 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1436840 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "График колебаний" "field_branch_order" => "39" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125} "field_page_start" => "182" "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 {#1124} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1123} ] #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 {#1038 #items: array:2 [ 0 => App\Models\Element {#1100 #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" => 1702553 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090 #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" => 6109 "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 {#1099 #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" => 5155 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Мнемозина" "field_cases" => null "field_translit" => "mnemozina" ] #original: array:6 [ "id" => 5155 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Мнемозина" "field_cases" => null "field_translit" => "mnemozina" ] #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_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 {#1096 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1095 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1094 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6109 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1097} "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 {#1096} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1095} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1094} "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" => "1437132" "type" => "task" ] "text" => "<p><strong>3.</strong> Сколько колебаний совершил маятник за 2,5 с (рис. 159)?</p><p>Рис. 159</p>" "img" => array:1 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1351" "height" => 764 "path" => "/media/fizika_09/shahmaev-u/0-39/3-1.webp?ts=1759448875" ] ] ] #original: array:7 [ "id" => 1702553 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090} "task" => array:2 [ "refs" => "1437132" "type" => "task" ] "text" => "<p><strong>3.</strong> Сколько колебаний совершил маятник за 2,5 с (рис. 159)?</p><p>Рис. 159</p>" "img" => array:1 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1351" "height" => 764 "path" => "/media/fizika_09/shahmaev-u/0-39/3-1.webp?ts=1759448875" ] ] ] #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 {#1092 #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" => 1732474 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1082 #items: array:1 [ 0 => App\Models\Edition {#1093 #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" => 6315 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1088 #items: array:1 [ 0 => App\Models\Term {#1091 #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" => 7012 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Gemini 2.5 Pro" "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" => "gemini 2.5 pro" ] #original: array:6 [ "id" => 7012 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Gemini 2.5 Pro" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null …2 ] "field_translit" => "gemini 2.5 pro" ] #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_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 {#1089 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1087 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6315 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1088} "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 {#1089} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1087} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1084} "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" => "1437132" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Время наблюдения $t = 2,5$ с</p><p>График зависимости смещения от времени (рис. 159)</p><p><strong>Найти:</strong></p><p>$\text{N}$ - ?</p><p><strong>Решение:</strong></p><p>На представленном графике показана зависимость смещения маятника $\text{x}$ от времени $\text{t}$. Чтобы найти количество колебаний $\text{N}$ за заданное время $\text{t}$, необходимо сначала определить период колебаний $\text{T}$ маятника, используя график.</p><p>Период колебаний $\text{T}$ – это минимальный промежуток времени, через который движение тела полностью повторяется. Его можно определить по графику как время одного полного колебания. Например, время между двумя последовательными максимумами (гребнями) или минимумами (впадинами) волны.</p><p>Из графика видно, что за 2 секунды маятник совершает ровно 2 полных колебания (например, от $t=0$ до $t=2$ с). Следовательно, время одного полного колебания (период) составляет:</p><p>$T = \frac{2 \text{ с}}{2} = 1 \text{ с}$</p><p>Теперь, зная период колебаний, можно найти количество колебаний $\text{N}$ за время $t = 2,5$ с по формуле:</p><p>$N = \frac{t}{T}$</p><p>Подставим известные значения в формулу:</p><p>$N = \frac{2,5 \text{ с}}{1 \text{ с}} = 2,5$</p><p>Таким образом, за 2,5 секунды маятник совершит 2,5 колебания.</p><p><strong>Ответ:</strong> 2,5.</p>" ] #original: array:6 [ "id" => 1732474 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1082} "task" => array:2 [ "refs" => "1437132" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Время наблюдения $t = 2,5$ с</p><p>График зависимости смещения от времени (рис. 159)</p><p><strong>Найти:</strong></p><p>$\text{N}$ - ?</p><p><strong>Решение:</strong></p><p>На представленном графике показана зависимость смещения маятника $\text{x}$ от времени $\text{t}$. Чтобы найти количество колебаний $\text{N}$ за заданное время $\text{t}$, необходимо сначала определить период колебаний $\text{T}$ маятника, используя график.</p><p>Период колебаний $\text{T}$ – это минимальный промежуток времени, через который движение тела полностью повторяется. Его можно определить по графику как время одного полного колебания. Например, время между двумя последовательными максимумами (гребнями) или минимумами (впадинами) волны.</p><p>Из графика видно, что за 2 секунды маятник совершает ровно 2 полных колебания (например, от $t=0$ до $t=2$ с). Следовательно, время одного полного колебания (период) составляет:</p><p>$T = \frac{2 \text{ с}}{2} = 1 \text{ с}$</p><p>Теперь, зная период колебаний, можно найти количество колебаний $\text{N}$ за время $t = 2,5$ с по формуле:</p><p>$N = \frac{t}{T}$</p><p>Подставим известные значения в формулу:</p><p>$N = \frac{2,5 \text{ с}}{1 \text{ с}} = 2,5$</p><p>Таким образом, за 2,5 секунды маятник совершит 2,5 колебания.</p><p><strong>Ответ:</strong> 2,5.</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" => "1437133" "type" => "task" ] "previous" => array:2 [ "refs" => "1437131" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\BookPage {#1105 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1436744 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "185" "field_url" => "/9-klass/fizika/shahmaev-uchebnik/page-185" "field_display_title" => "185" "field_folder" => "1" "field_image_name" => "185" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1085 #items: array:1 [ 0 => App\Models\Book {#1049} ] #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 {#1083 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1112 #items: array:1 [ 0 => App\Models\Element {#1116 #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" => 1702820 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:1 [ 0 => App\Models\Edition {#1098} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1436744" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "185-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_09/shahmaev-u/0-1/185-1.webp?ts=1759449136" ] ] ] #original: array:6 [ "id" => 1702820 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1110} "book_page" => array:2 [ "refs" => "1436744" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "185-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_09/shahmaev-u/0-1/185-1.webp?ts=1759449136" ] ] ] #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" => "1436745" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1436743" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1186 #items: array:4 [ 0 => App\Models\Task {#1196 #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" => 1437130 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "185" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/39-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1197 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1198 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1199 #items: array:1 [ 0 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1200 #items: array:2 [ 0 => App\Models\Branch {#1117} 1 => App\Models\Branch {#1121} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1202 #items: array:2 [ 0 => App\Models\Element {#1211 #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" => 1702551 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1212 …2} "task" => array:2 [ …2] "text" => "<p><strong>1.</strong> Какая кривая является графиком незатухающих свободных колебаний маятников и ветвей камертона?</p>" "img" => array:1 [ …1] ] #original: array:7 [ "id" => 1702551 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1212 …2} "task" => array:2 [ …2] "text" => "<p><strong>1.</strong> Какая кривая является графиком незатухающих свободных колебаний маятников и ветвей камертона?</p>" "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 => "*" ] } 1 => App\Models\Element {#1213 #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" => 1732472 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "task" => array:2 [ …2] "text" => "<p><strong>1.</strong> Графиком незатухающих свободных колебаний, которые также называют гармоническими колебаниями, является кривая, называемая синусоидой (или косинусоидой). Колебания маятников (при малых углах отклонения) и ветвей камертона в идеализированной модели, где отсутствуют силы трения и сопротивления, описываются законом синуса или косинуса. Математически это выражается уравнением гармонических колебаний: $x(t) = A \cos(\omega t + \phi_0)$, где $x(t)$ — смещение колеблющейся точки от положения равновесия в момент времени $\text{t}$, $\text{A}$ — амплитуда колебаний (максимальное смещение), $\omega$ — циклическая (круговая) частота, а $(\omega t + \phi_0)$ — фаза колебаний в момент времени $\text{t}$ ($\phi_0$ — начальная фаза). График такой функции, показывающий зависимость смещения от времени, представляет собой синусоиду.</p><p><strong>Ответ:</strong> Синусоида (или косинусоида).</p>" ] #original: array:6 [ "id" => 1732472 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "task" => array:2 [ …2] "text" => "<p><strong>1.</strong> Графиком незатухающих свободных колебаний, которые также называют гармоническими колебаниями, является кривая, называемая синусоидой (или косинусоидой). Колебания маятников (при малых углах отклонения) и ветвей камертона в идеализированной модели, где отсутствуют силы трения и сопротивления, описываются законом синуса или косинуса. Математически это выражается уравнением гармонических колебаний: $x(t) = A \cos(\omega t + \phi_0)$, где $x(t)$ — смещение колеблющейся точки от положения равновесия в момент времени $\text{t}$, $\text{A}$ — амплитуда колебаний (максимальное смещение), $\omega$ — циклическая (круговая) частота, а $(\omega t + \phi_0)$ — фаза колебаний в момент времени $\text{t}$ ($\phi_0$ — начальная фаза). График такой функции, показывающий зависимость смещения от времени, представляет собой синусоиду.</p><p><strong>Ответ:</strong> Синусоида (или косинусоида).</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" => "1437131" "type" => "task" ] "previous" => array:2 [ "refs" => "1437129" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1208 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1436744" "type" => "book_page" ] ] #original: array:24 [ "id" => 1437130 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "185" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/39-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1197} "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 {#1198} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1199} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1200} "content" => Illuminate\Database\Eloquent\Collection {#1202} "next" => array:2 [ "refs" => "1437131" "type" => "task" ] "previous" => array:2 [ "refs" => "1437129" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1208} "page" => array:2 [ "refs" => "1436744" "type" => "book_page" ] ] #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\Task {#1203 #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" => 1437131 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "185" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/39-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1201 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1210 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1206 #items: array:1 [ 0 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1204 #items: array:2 [ 0 => App\Models\Branch {#1117} 1 => App\Models\Branch {#1121} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1205 #items: array:2 [ 0 => App\Models\Element {#1223 #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" => 1702552 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1224 …2} "task" => array:2 [ …2] "text" => "<p><strong>2.</strong> По графику колебаний, приведенному на рисунке 159, определите период, амплитуду и размах колебаний маятника.</p>" "img" => array:1 [ …1] ] #original: array:7 [ "id" => 1702552 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1224 …2} "task" => array:2 [ …2] "text" => "<p><strong>2.</strong> По графику колебаний, приведенному на рисунке 159, определите период, амплитуду и размах колебаний маятника.</p>" "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 => "*" ] } 1 => App\Models\Element {#1225 #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" => 1732473 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1226 …2} "task" => array:2 [ …2] "text" => "<p>Поскольку график колебаний (рисунок 159), необходимый для решения задачи, не предоставлен, приведем общий алгоритм нахождения искомых величин на основе стандартного графика зависимости смещения от времени.</p><p><strong>Дано:</strong></p><p>График зависимости смещения маятника от времени $x(t)$.</p><p><strong>Найти:</strong></p><p>Период $\text{T}$ — ?</p><p>Амплитуда $\text{A}$ — ?</p><p>Размах колебаний — ?</p><p><strong>Решение:</strong></p><p><strong>период</strong></p><p>Период колебаний ($\text{T}$) — это время одного полного колебания. На графике это промежуток времени между двумя последовательными точками, находящимися в одинаковой фазе, например, между двумя соседними пиками (максимумами) или двумя соседними впадинами (минимумами). Чтобы найти период, нужно взять на оси времени $\text{t}$ значения, соответствующие этим точкам (например, $t_1$ и $t_2$), и вычислить разность: $T = t_2 - t_1$.</p><p><strong>Ответ:</strong> Период колебаний $\text{T}$ равен значению, определенному по оси времени графика, в секундах.</p><p><strong>амплитуду</strong></p><p>Амплитуда колебаний ($\text{A}$) — это модуль максимального смещения тела от положения равновесия. На графике это максимальное значение по вертикальной оси (оси смещения), которого достигает колеблющееся тело. Если положение равновесия соответствует нулевой отметке на оси, то амплитуда равна координате самой высокой точки графика: $A = |x_{max}|$.</p><p><strong>Ответ:</strong> Амплитуда колебаний $\text{A}$ равна значению, определенному по оси смещения графика, в метрах (или других единицах длины, указанных на оси).</p><p><strong>размах колебаний</strong></p><p>Размах колебаний — это расстояние между крайними положениями колеблющегося тела. Он равен удвоенной амплитуде. На графике это разница между максимальным и минимальным значением смещения: $Размах = x_{max} - x_{min}$. Так как для симметричных колебаний $x_{min} = -x_{max} = -A$, то размах вычисляется по формуле: $Размах = A - (-A) = 2A$.</p><p><strong>Ответ:</strong> Размах колебаний равен удвоенному значению определенной по графику амплитуды.</p>" ] #original: array:6 [ "id" => 1732473 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1226 …2} "task" => array:2 [ …2] "text" => "<p>Поскольку график колебаний (рисунок 159), необходимый для решения задачи, не предоставлен, приведем общий алгоритм нахождения искомых величин на основе стандартного графика зависимости смещения от времени.</p><p><strong>Дано:</strong></p><p>График зависимости смещения маятника от времени $x(t)$.</p><p><strong>Найти:</strong></p><p>Период $\text{T}$ — ?</p><p>Амплитуда $\text{A}$ — ?</p><p>Размах колебаний — ?</p><p><strong>Решение:</strong></p><p><strong>период</strong></p><p>Период колебаний ($\text{T}$) — это время одного полного колебания. На графике это промежуток времени между двумя последовательными точками, находящимися в одинаковой фазе, например, между двумя соседними пиками (максимумами) или двумя соседними впадинами (минимумами). Чтобы найти период, нужно взять на оси времени $\text{t}$ значения, соответствующие этим точкам (например, $t_1$ и $t_2$), и вычислить разность: $T = t_2 - t_1$.</p><p><strong>Ответ:</strong> Период колебаний $\text{T}$ равен значению, определенному по оси времени графика, в секундах.</p><p><strong>амплитуду</strong></p><p>Амплитуда колебаний ($\text{A}$) — это модуль максимального смещения тела от положения равновесия. На графике это максимальное значение по вертикальной оси (оси смещения), которого достигает колеблющееся тело. Если положение равновесия соответствует нулевой отметке на оси, то амплитуда равна координате самой высокой точки графика: $A = |x_{max}|$.</p><p><strong>Ответ:</strong> Амплитуда колебаний $\text{A}$ равна значению, определенному по оси смещения графика, в метрах (или других единицах длины, указанных на оси).</p><p><strong>размах колебаний</strong></p><p>Размах колебаний — это расстояние между крайними положениями колеблющегося тела. Он равен удвоенной амплитуде. На графике это разница между максимальным и минимальным значением смещения: $Размах = x_{max} - x_{min}$. Так как для симметричных колебаний $x_{min} = -x_{max} = -A$, то размах вычисляется по формуле: $Размах = A - (-A) = 2A$.</p><p><strong>Ответ:</strong> Размах колебаний равен удвоенному значению определенной по графику амплитуды.</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" => "1437132" "type" => "task" ] "previous" => array:2 [ "refs" => "1437130" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1220 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1436744" "type" => "book_page" ] ] #original: array:24 [ "id" => 1437131 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "185" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/39-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1201} "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 {#1210} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1206} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1204} "content" => Illuminate\Database\Eloquent\Collection {#1205} "next" => array:2 [ "refs" => "1437132" "type" => "task" ] "previous" => array:2 [ "refs" => "1437130" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1220} "page" => array:2 [ "refs" => "1436744" "type" => "book_page" ] ] #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\Task {#1215 #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" => 1437132 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "185" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/39-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1207 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1222 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1218 #items: array:1 [ 0 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1216 #items: array:2 [ 0 => App\Models\Branch {#1117} 1 => App\Models\Branch {#1121} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1219 #items: array:2 [ 0 => App\Models\Element {#1100} 1 => App\Models\Element {#1092} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1437133" "type" => "task" ] "previous" => array:2 [ "refs" => "1437131" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1217 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1436744" "type" => "book_page" ] ] #original: array:24 [ "id" => 1437132 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "185" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/39-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1207} "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 {#1222} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1218} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1216} "content" => Illuminate\Database\Eloquent\Collection {#1219} "next" => array:2 [ "refs" => "1437133" "type" => "task" ] "previous" => array:2 [ "refs" => "1437131" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1217} "page" => array:2 [ "refs" => "1436744" "type" => "book_page" ] ] #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\Task {#1227 #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" => 1437133 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "185" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/39-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1228 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1229 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1230 #items: array:1 [ 0 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1231 #items: array:2 [ 0 => App\Models\Branch {#1117} 1 => App\Models\Branch {#1121} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1233 #items: array:2 [ 0 => App\Models\Element {#1242 #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" => 1702554 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1243 …2} "task" => array:2 [ …2] "text" => "<p><strong>4.</strong> Какую часть периода составило время движения маятника, если он отклонился от положения равновесия до крайнего положения? дошел до крайнего положения и вернулся в положение равновесия?</p>" "img" => array:1 [ …1] ] #original: array:7 [ "id" => 1702554 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1243 …2} "task" => array:2 [ …2] "text" => "<p><strong>4.</strong> Какую часть периода составило время движения маятника, если он отклонился от положения равновесия до крайнего положения? дошел до крайнего положения и вернулся в положение равновесия?</p>" "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 => "*" ] } 1 => App\Models\Element {#1244 #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" => 1732475 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1245 …2} "task" => array:2 [ …2] "text" => "<p><strong>Решение</strong></p><p>Период колебаний $\text{T}$ — это минимальный промежуток времени, через который система, совершающая колебания, возвращается в то же состояние, в котором она находилась в начальный момент времени. Для маятника это означает, что он должен вернуться в исходную точку с той же скоростью (и направлением).<br>Полное колебание маятника можно условно разделить на четыре равных по времени этапа:<br>1. Движение из положения равновесия до одного крайнего положения (например, вправо).<br>2. Движение из этого крайнего положения обратно в положение равновесия.<br>3. Движение из положения равновесия до другого крайнего положения (влево).<br>4. Движение из второго крайнего положения обратно в положение равновесия.<br>Каждый из этих этапов длится одинаковое время, равное одной четверти периода, то есть $t = \frac{T}{4}$.</p><p><strong>...если он отклонился от положения равновесия до крайнего положения?</strong><br>Движение маятника от положения равновесия до крайнего положения представляет собой ровно один из четырех описанных выше этапов. Следовательно, время этого движения составляет одну четверть полного периода колебаний.<br>$t_1 = \frac{T}{4}$.<br>Таким образом, время движения составляет $\frac{1}{4}$ часть периода.<br><strong>Ответ:</strong> $\frac{1}{4}$ периода.</p><p><strong>...дошел до крайнего положения и вернулся в положение равновесия?</strong><br>В этом случае движение маятника состоит из двух последовательных этапов:<br>1. Движение от положения равновесия до крайнего положения, время которого равно $\frac{T}{4}$.<br>2. Движение от крайнего положения обратно в положение равновесия, время которого также равно $\frac{T}{4}$.<br>Общее время движения будет суммой времени этих двух этапов:<br>$t_2 = \frac{T}{4} + \frac{T}{4} = \frac{2T}{4} = \frac{T}{2}$.<br>Таким образом, время движения составляет $\frac{1}{2}$ часть периода.<br><strong>Ответ:</strong> $\frac{1}{2}$ периода.</p>" ] #original: array:6 [ "id" => 1732475 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1245 …2} "task" => array:2 [ …2] "text" => "<p><strong>Решение</strong></p><p>Период колебаний $\text{T}$ — это минимальный промежуток времени, через который система, совершающая колебания, возвращается в то же состояние, в котором она находилась в начальный момент времени. Для маятника это означает, что он должен вернуться в исходную точку с той же скоростью (и направлением).<br>Полное колебание маятника можно условно разделить на четыре равных по времени этапа:<br>1. Движение из положения равновесия до одного крайнего положения (например, вправо).<br>2. Движение из этого крайнего положения обратно в положение равновесия.<br>3. Движение из положения равновесия до другого крайнего положения (влево).<br>4. Движение из второго крайнего положения обратно в положение равновесия.<br>Каждый из этих этапов длится одинаковое время, равное одной четверти периода, то есть $t = \frac{T}{4}$.</p><p><strong>...если он отклонился от положения равновесия до крайнего положения?</strong><br>Движение маятника от положения равновесия до крайнего положения представляет собой ровно один из четырех описанных выше этапов. Следовательно, время этого движения составляет одну четверть полного периода колебаний.<br>$t_1 = \frac{T}{4}$.<br>Таким образом, время движения составляет $\frac{1}{4}$ часть периода.<br><strong>Ответ:</strong> $\frac{1}{4}$ периода.</p><p><strong>...дошел до крайнего положения и вернулся в положение равновесия?</strong><br>В этом случае движение маятника состоит из двух последовательных этапов:<br>1. Движение от положения равновесия до крайнего положения, время которого равно $\frac{T}{4}$.<br>2. Движение от крайнего положения обратно в положение равновесия, время которого также равно $\frac{T}{4}$.<br>Общее время движения будет суммой времени этих двух этапов:<br>$t_2 = \frac{T}{4} + \frac{T}{4} = \frac{2T}{4} = \frac{T}{2}$.<br>Таким образом, время движения составляет $\frac{1}{2}$ часть периода.<br><strong>Ответ:</strong> $\frac{1}{2}$ периода.</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" => "1437134" "type" => "task" ] "previous" => array:2 [ "refs" => "1437132" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1239 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1436744" "type" => "book_page" ] ] #original: array:24 [ "id" => 1437133 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "185" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/39-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1228} "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 {#1229} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1230} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1231} "content" => Illuminate\Database\Eloquent\Collection {#1233} "next" => array:2 [ "refs" => "1437134" "type" => "task" ] "previous" => array:2 [ "refs" => "1437132" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1239} "page" => array:2 [ "refs" => "1436744" "type" => "book_page" ] ] #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:21 [ "id" => 1436744 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "185" "field_url" => "/9-klass/fizika/shahmaev-uchebnik/page-185" "field_display_title" => "185" "field_folder" => "1" "field_image_name" => "185" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1086} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1085} "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 {#1083} "content" => Illuminate\Database\Eloquent\Collection {#1112} "next" => array:2 [ "refs" => "1436745" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1436743" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1186} ] #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" => 1437132 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "185" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/39-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "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} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1109} "content" => Illuminate\Database\Eloquent\Collection {#1038} "next" => array:2 [ "refs" => "1437133" "type" => "task" ] "previous" => array:2 [ "refs" => "1437131" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1103} "page" => array:2 [ "refs" => "1436744" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№3 (с. 185)
Условие. №3 (с. 185)
скриншот условия
3. Сколько колебаний совершил маятник за 2,5 с (рис. 159)?
Рис. 159
Решение. №3 (с. 185)
Дано:
Время наблюдения $t = 2,5$ с
График зависимости смещения от времени (рис. 159)
Найти:
$\text{N}$ - ?
Решение:
На представленном графике показана зависимость смещения маятника $\text{x}$ от времени $\text{t}$. Чтобы найти количество колебаний $\text{N}$ за заданное время $\text{t}$, необходимо сначала определить период колебаний $\text{T}$ маятника, используя график.
Период колебаний $\text{T}$ – это минимальный промежуток времени, через который движение тела полностью повторяется. Его можно определить по графику как время одного полного колебания. Например, время между двумя последовательными максимумами (гребнями) или минимумами (впадинами) волны.
Из графика видно, что за 2 секунды маятник совершает ровно 2 полных колебания (например, от $t=0$ до $t=2$ с). Следовательно, время одного полного колебания (период) составляет:
$T = \frac{2 \text{ с}}{2} = 1 \text{ с}$
Теперь, зная период колебаний, можно найти количество колебаний $\text{N}$ за время $t = 2,5$ с по формуле:
$N = \frac{t}{T}$
Подставим известные значения в формулу:
$N = \frac{2,5 \text{ с}}{1 \text{ с}} = 2,5$
Таким образом, за 2,5 секунды маятник совершит 2,5 колебания.
Ответ: 2,5.
Другие задания:
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