gdz.top
Задание 1, страница 201, часть 1 - гдз по физике 9 класс учебник Генденштейн, Булатова
Авторы: Генденштейн Л. Э., Булатова А. А., Корнильев И. Н., Кошкина А. В.
Тип: Учебник
Издательство: Бином
Год издания: 2016 - 2026
Часть: 1
Цвет обложки: бирюзовый
ISBN: 978-5-9963-3062-1
Популярные ГДЗ в 9 классе
Часть 1. Лабораторные работы. 7. Изучение колебаний пружинного маятника - страница 201.
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" => 1433922 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "201" "field_page_end" => "202" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/labrab7-1" "field_display_title" => "Задание 1" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1036 #items: [] #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 {#1034 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:1 [ 0 => App\Models\Branch {#1035 #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" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Term {#1037 #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" => "6" "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 {#1039 #items: array:1 [ 0 => App\Models\Book {#1040 #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" => 2980 "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 {#1041 #items: array:1 [ 0 => App\Models\Term {#1042 #connection: "mysql" …29 } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\Term {#1044 …30} ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ 0 => App\Models\Term {#1046 …30} ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:4 [ 0 => App\Models\Term {#1048 …30} 1 => App\Models\Term {#1049 …30} 2 => App\Models\Term {#1050 …30} 3 => App\Models\Term {#1051 …30} ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 #items: array:1 [ 0 => App\Models\Term {#1054 …30} ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1055 #items: array:1 [ 0 => App\Models\Term {#1056 …30} ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1057 #items: array:1 [ 0 => App\Models\Term {#1058 …30} ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 …30} ] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "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" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ 0 => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" 1 => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" ] "field_cover_alts" => array:2 [ 0 => "" 1 => "" ] "field_covers" => array:2 [ 0 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2813" ] 1 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2809" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1069 #items: array:1 [ 0 => App\Models\Term {#1070 …30} ] #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" => 2980 "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 {#1041} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045} "field_author" => Illuminate\Database\Eloquent\Collection {#1047} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053} "field_country" => Illuminate\Database\Eloquent\Collection {#1055} "field_city" => Illuminate\Database\Eloquent\Collection {#1057} "field_series" => Illuminate\Database\Eloquent\Collection {#1059} "field_umk" => Illuminate\Database\Eloquent\Collection {#1060} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1062} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1063} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "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" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ 0 => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" 1 => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" ] "field_cover_alts" => array:2 [ 0 => "" 1 => "" ] "field_covers" => array:2 [ 0 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2813" ] 1 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2809" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1066} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1067} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1068} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1069} "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 {#1071 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1038} "field_page_start" => "6" "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 {#1039} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1071} ] #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 {#1110 #items: array:3 [ 0 => App\Models\Branch {#1120 #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" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1124 #items: array:1 [ 0 => App\Models\Term {#1121 #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" => "6" "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 {#1156 #items: array:1 [ 0 => App\Models\Book {#1123 #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" => 2980 "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 {#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: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 {#1126 #items: array:1 [ 0 => App\Models\Term {#1127 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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 {#1128 #items: array:1 [ 0 => App\Models\Term {#1129 #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" => 5208 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бином" "field_cases" => null "field_translit" => "binom" ] #original: array:6 [ "id" => 5208 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бином" "field_cases" => null "field_translit" => "binom" ] #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 {#1130 #items: array:4 [ 0 => App\Models\Term {#1131 #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" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #original: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #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 {#1132 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 3936 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Булатова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Альбина" "field_patronymic" => "Александрова" "field_surname_rp" => null ] #original: array:12 [ "id" => 3936 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Булатова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Альбина" "field_patronymic" => "Александрова" "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 {#1133 #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" => 4679 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Корнильев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Игорь" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4679 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Корнильев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Игорь" "field_patronymic" => "Николаевич" "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 {#1134 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4758 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кошкина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Анжелика" "field_patronymic" => "Васильевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4758 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кошкина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Анжелика" "field_patronymic" => "Васильевна" "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 {#1135 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1136 #items: array:1 [ 0 => App\Models\Term {#1137 #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 {#1138 #items: array:1 [ 0 => App\Models\Term {#1139 #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 {#1140 #items: array:1 [ 0 => App\Models\Term {#1141 #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 {#1142 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1143 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1144 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1147 #items: array:1 [ 0 => App\Models\Term {#1148 #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" => 5395 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Орлов" "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" => "Алексеевич" "field_surname_rp" => "Орлова" ] #original: array:12 [ "id" => 5395 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Орлов" "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" => "Алексеевич" "field_surname_rp" => "Орлова" ] #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_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "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" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ 0 => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" 1 => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" ] "field_cover_alts" => array:2 [ 0 => "" 1 => "" ] "field_covers" => array:2 [ 0 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2813" ] 1 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2809" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1149 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1150 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1151 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1152 #items: array:1 [ 0 => App\Models\Term {#1153 #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" => 6978 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "бирюзовый" "field_cases" => array:6 [ "field_accusative_case" => "бирюзовый" "field_creative_case" => "бирюзовым" "field_dative_case" => "бирюзовому" "field_genitive_case" => "бирюзового" "field_nominative_case" => "бирюзовый" "field_prepositional_case" => "бирюзовом" ] "field_translit" => "biruzovyy" ] #original: array:6 [ "id" => 6978 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "бирюзовый" "field_cases" => array:6 [ "field_accusative_case" => "бирюзовый" "field_creative_case" => "бирюзовым" "field_dative_case" => "бирюзовому" "field_genitive_case" => "бирюзового" "field_nominative_case" => "бирюзовый" "field_prepositional_case" => "бирюзовом" ] "field_translit" => "biruzovyy" ] #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" => 2980 "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 {#1125} "field_class" => Illuminate\Database\Eloquent\Collection {#1126} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1128} "field_author" => Illuminate\Database\Eloquent\Collection {#1130} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1135} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1136} "field_country" => Illuminate\Database\Eloquent\Collection {#1138} "field_city" => Illuminate\Database\Eloquent\Collection {#1140} "field_series" => Illuminate\Database\Eloquent\Collection {#1142} "field_umk" => Illuminate\Database\Eloquent\Collection {#1143} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1144} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1145} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1146} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1147} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "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" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ 0 => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" 1 => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" ] "field_cover_alts" => array:2 [ 0 => "" 1 => "" ] "field_covers" => array:2 [ 0 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2813" ] 1 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2809" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1149} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1150} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1151} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1152} "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 {#1154 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1124} "field_page_start" => "6" "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 {#1156} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1154} ] #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 {#1155 #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" => 1433234 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1157 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "194" "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 {#1158 #items: array:1 [ 0 => App\Models\Book {#1123} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1159 #items: array:1 [ 0 => App\Models\Branch {#1035} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1433234 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1157} "field_page_start" => "194" "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 {#1158} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1159} ] #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 {#1160 #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" => 1433241 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7. Изучение колебаний пружинного маятника" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1161 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "201" "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 {#1162 #items: array:1 [ 0 => App\Models\Book {#1123} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1171 #items: array:1 [ 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" => 1433234 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1172 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "194" "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 {#1173 #items: array:1 [ 0 => App\Models\Book {#1123} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1174 #items: array:1 [ 0 => App\Models\Branch {#1035} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1433234 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1172} "field_page_start" => "194" "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 {#1173} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1174} ] #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" => 1433241 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7. Изучение колебаний пружинного маятника" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1161} "field_page_start" => "201" "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 {#1162} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1171} ] #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 {#1072 #items: array:2 [ 0 => App\Models\Element {#1101 #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" => 1697086 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1092 #items: array:1 [ 0 => App\Models\Edition {#1102 #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" => 6168 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1099 #items: array:1 [ 0 => App\Models\Term {#1100 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1098 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1097 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1096 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6168 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1099} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1098} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1097} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1096} "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" => "1433922" "type" => "task" ] "text" => "<p><strong>7. Изучение колебаний пружинного маятника</strong></p><p><strong><em>Цель работы: </em></strong>исследовать зависимость периода колебаний груза на пружине от амплитуды колебаний, жёсткости пружины и массы груза; определить частоту колебаний груза.</p><p><strong><em>Оборудование: </em></strong>штатив, две пружины различной жёсткости1), набор грузов по механике массой по 100 г, секундомер или часы с секундной стрелкой.</p><p><strong>Ход работы</strong></p><p><strong>Задание 1. Исследование зависимости периода колебаний пружинного маятника от амплитуды.</strong></p><p>• Подвесьте пружину к штативу, а к пружине подвесьте один груз. Отведите груз вниз от положения равновесия примерно на 1 см и отпустите. Измерьте промежуток времени $t_1$, за который совершается 10 полных колебаний. Результат запишите с указанием погрешности в таблицу (ниже приведён заголовок таблицы).</p><p>N | $t_1$, с | $T_1$, с | $t_2$, с | $T_2$, с</p><p>• Запишите формулу для расчёта периода колебаний $T_1$ и найдите значение периода. Запишите результат с указанием погрешности1) в таблицу.</p><p>• Повторите опыт, увеличив амплитуду колебаний примерно в 2 раза. Запишите соответствующий промежуток времени $t_2$, вычислите период колебаний $T_2$. Результат запишите с указанием погрешности в таблицу.</p><p>• Сделайте вывод о зависимости или независимости периода колебаний пружинного маятника от амплитуды колебаний.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1614" "height" => 827 "path" => "/media/fizika_09/gendenshtejn-u/0-labrab7/1-1.webp?ts=1759348497" ] 1 => array:5 [ "name" => "1-2.jpg" "alt" => null "width" => "1590" "height" => 823 "path" => "/media/fizika_09/gendenshtejn-u/0-labrab7/1-2.webp?ts=1759348497" ] ] ] #original: array:7 [ "id" => 1697086 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1092} "task" => array:2 [ "refs" => "1433922" "type" => "task" ] "text" => "<p><strong>7. Изучение колебаний пружинного маятника</strong></p><p><strong><em>Цель работы: </em></strong>исследовать зависимость периода колебаний груза на пружине от амплитуды колебаний, жёсткости пружины и массы груза; определить частоту колебаний груза.</p><p><strong><em>Оборудование: </em></strong>штатив, две пружины различной жёсткости1), набор грузов по механике массой по 100 г, секундомер или часы с секундной стрелкой.</p><p><strong>Ход работы</strong></p><p><strong>Задание 1. Исследование зависимости периода колебаний пружинного маятника от амплитуды.</strong></p><p>• Подвесьте пружину к штативу, а к пружине подвесьте один груз. Отведите груз вниз от положения равновесия примерно на 1 см и отпустите. Измерьте промежуток времени $t_1$, за который совершается 10 полных колебаний. Результат запишите с указанием погрешности в таблицу (ниже приведён заголовок таблицы).</p><p>N | $t_1$, с | $T_1$, с | $t_2$, с | $T_2$, с</p><p>• Запишите формулу для расчёта периода колебаний $T_1$ и найдите значение периода. Запишите результат с указанием погрешности1) в таблицу.</p><p>• Повторите опыт, увеличив амплитуду колебаний примерно в 2 раза. Запишите соответствующий промежуток времени $t_2$, вычислите период колебаний $T_2$. Результат запишите с указанием погрешности в таблицу.</p><p>• Сделайте вывод о зависимости или независимости периода колебаний пружинного маятника от амплитуды колебаний.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1614" "height" => 827 "path" => "/media/fizika_09/gendenshtejn-u/0-labrab7/1-1.webp?ts=1759348497" ] 1 => array:5 [ "name" => "1-2.jpg" "alt" => null "width" => "1590" "height" => 823 "path" => "/media/fizika_09/gendenshtejn-u/0-labrab7/1-2.webp?ts=1759348497" ] ] ] #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 {#1094 #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" => 1781156 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1086 #items: array:1 [ 0 => App\Models\Edition {#1095 #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" => 6515 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Term {#1093 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "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 {#1091 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1089 #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" => 6515 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1090} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "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 {#1091} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1089} "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" => "1433922" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Число полных колебаний: $N = 10$</p><p>Для проведения мысленного эксперимента возьмем следующие правдоподобные результаты измерений:</p><p>Время 10 колебаний при амплитуде $A_1 \approx 1$ см: $t_1 = 6,3$ с</p><p>Время 10 колебаний при амплитуде $A_2 \approx 2$ см: $t_2 = 6,4$ с</p><p>Абсолютная погрешность измерения времени секундомером (с учетом реакции экспериментатора): $\Delta t = 0,2$ с</p><p>Все данные представлены в системе СИ.</p><p><strong>Найти:</strong></p><p><strong>1.</strong> Период колебаний $T_1$ и его погрешность $\Delta T_1$.</p><p><strong>2.</strong> Период колебаний $T_2$ и его погрешность $\Delta T_2$.</p><p><strong>3.</strong> Сделать вывод о зависимости периода колебаний от амплитуды.</p><p><strong>Решение:</strong></p><p>Результаты измерений и вычислений, полученные в ходе выполнения работы, сведены в таблицу:</p><table><thead><tr><th style="padding: 5px; text-align: center;">N</th><th style="padding: 5px; text-align: center;">$t_1$, с</th><th style="padding: 5px; text-align: center;">$T_1$, с</th><th style="padding: 5px; text-align: center;">$t_2$, с</th><th style="padding: 5px; text-align: center;">$T_2$, с</th></tr></thead><tbody><tr><td style="padding: 5px; text-align: center;">10</td><td style="padding: 5px; text-align: center;">$6,3 \pm 0,2$</td><td style="padding: 5px; text-align: center;">$0,63 \pm 0,02$</td><td style="padding: 5px; text-align: center;">$6,4 \pm 0,2$</td><td style="padding: 5px; text-align: center;">$0,64 \pm 0,02$</td></tr></tbody></table><p>Ниже представлены расчеты, на основе которых была заполнена таблица.</p><p><strong>Запишите формулу для расчёта периода колебаний T₁ и найдите значение периода. Запишите результат с указанием погрешности¹) в таблицу.</strong></p><p>Период колебаний $\text{T}$ – это время одного полного колебания. Для его нахождения необходимо общее время колебаний $\text{t}$ разделить на число совершенных за это время полных колебаний $\text{N}$.</p><p>Формула для расчёта периода:</p><p>$T = \frac{t}{N}$</p><p>Вычислим период для первого опыта:</p><p>$T_1 = \frac{t_1}{N} = \frac{6,3 \text{ с}}{10} = 0,63 \text{ с}$</p><p>Абсолютная погрешность измерения периода вычисляется по формуле $\Delta T = \frac{\Delta t}{N}$, так как число колебаний $\text{N}$ является точной величиной.</p><p>$\Delta T_1 = \frac{0,2 \text{ с}}{10} = 0,02 \text{ с}$</p><p>Таким образом, результат для первого периода с учетом погрешности:</p><p>$T_1 = (0,63 \pm 0,02)$ с</p><p><strong>Ответ:</strong> Формула для расчёта периода: $T = \frac{t}{N}$. Значение периода для первого опыта: $T_1 = (0,63 \pm 0,02)$ с.</p><p><strong>Повторите опыт, увеличив амплитуду колебаний примерно в 2 раза. Запишите соответствующий промежуток времени t₂, вычислите период колебаний Т₂. Результат запишите с указанием погрешности в таблицу.</strong></p><p>Вычислим период для второго опыта, используя время $t_2 = 6,4$ с:</p><p>$T_2 = \frac{t_2}{N} = \frac{6,4 \text{ с}}{10} = 0,64 \text{ с}$</p><p>Погрешность измерения периода во втором опыте рассчитывается аналогично и имеет то же значение, так как условия измерения не изменились:</p><p>$\Delta T_2 = \frac{0,2 \text{ с}}{10} = 0,02 \text{ с}$</p><p>Результат для второго периода с учетом погрешности:</p><p>$T_2 = (0,64 \pm 0,02)$ с</p><p><strong>Ответ:</strong> Значение периода для второго опыта: $T_2 = (0,64 \pm 0,02)$ с.</p><p><strong>Сделайте вывод о зависимости или независимости периода колебаний пружинного маятника от амплитуды колебаний.</strong></p><p>Для вывода сравним полученные значения периодов: $T_1 = (0,63 \pm 0,02)$ с и $T_2 = (0,64 \pm 0,02)$ с. Разница между средними значениями периодов составляет $|T_2 - T_1| = |0,64 - 0,63| = 0,01$ с. Эта разница меньше, чем погрешность измерений каждого из периодов ($\Delta T = 0,02$ с). Это означает, что измеренные значения согласуются друг с другом в пределах погрешности. Проверим пересечение доверительных интервалов:</p><p>Интервал для $T_1$: $[0,63 - 0,02; 0,63 + 0,02] = [0,61\text{ с}; 0,65\text{ с}]$</p><p>Интервал для $T_2$: $[0,64 - 0,02; 0,64 + 0,02] = [0,62\text{ с}; 0,66\text{ с}]$</p><p>Поскольку интервалы возможных значений периодов пересекаются, можно сделать вывод, что период колебаний не изменился при увеличении амплитуды в 2 раза.</p><p><strong>Ответ:</strong> Период колебаний пружинного маятника в пределах погрешности измерений не зависит от амплитуды колебаний (при малых амплитудах).</p>" ] #original: array:6 [ "id" => 1781156 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1086} "task" => array:2 [ "refs" => "1433922" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Число полных колебаний: $N = 10$</p><p>Для проведения мысленного эксперимента возьмем следующие правдоподобные результаты измерений:</p><p>Время 10 колебаний при амплитуде $A_1 \approx 1$ см: $t_1 = 6,3$ с</p><p>Время 10 колебаний при амплитуде $A_2 \approx 2$ см: $t_2 = 6,4$ с</p><p>Абсолютная погрешность измерения времени секундомером (с учетом реакции экспериментатора): $\Delta t = 0,2$ с</p><p>Все данные представлены в системе СИ.</p><p><strong>Найти:</strong></p><p><strong>1.</strong> Период колебаний $T_1$ и его погрешность $\Delta T_1$.</p><p><strong>2.</strong> Период колебаний $T_2$ и его погрешность $\Delta T_2$.</p><p><strong>3.</strong> Сделать вывод о зависимости периода колебаний от амплитуды.</p><p><strong>Решение:</strong></p><p>Результаты измерений и вычислений, полученные в ходе выполнения работы, сведены в таблицу:</p><table><thead><tr><th style="padding: 5px; text-align: center;">N</th><th style="padding: 5px; text-align: center;">$t_1$, с</th><th style="padding: 5px; text-align: center;">$T_1$, с</th><th style="padding: 5px; text-align: center;">$t_2$, с</th><th style="padding: 5px; text-align: center;">$T_2$, с</th></tr></thead><tbody><tr><td style="padding: 5px; text-align: center;">10</td><td style="padding: 5px; text-align: center;">$6,3 \pm 0,2$</td><td style="padding: 5px; text-align: center;">$0,63 \pm 0,02$</td><td style="padding: 5px; text-align: center;">$6,4 \pm 0,2$</td><td style="padding: 5px; text-align: center;">$0,64 \pm 0,02$</td></tr></tbody></table><p>Ниже представлены расчеты, на основе которых была заполнена таблица.</p><p><strong>Запишите формулу для расчёта периода колебаний T₁ и найдите значение периода. Запишите результат с указанием погрешности¹) в таблицу.</strong></p><p>Период колебаний $\text{T}$ – это время одного полного колебания. Для его нахождения необходимо общее время колебаний $\text{t}$ разделить на число совершенных за это время полных колебаний $\text{N}$.</p><p>Формула для расчёта периода:</p><p>$T = \frac{t}{N}$</p><p>Вычислим период для первого опыта:</p><p>$T_1 = \frac{t_1}{N} = \frac{6,3 \text{ с}}{10} = 0,63 \text{ с}$</p><p>Абсолютная погрешность измерения периода вычисляется по формуле $\Delta T = \frac{\Delta t}{N}$, так как число колебаний $\text{N}$ является точной величиной.</p><p>$\Delta T_1 = \frac{0,2 \text{ с}}{10} = 0,02 \text{ с}$</p><p>Таким образом, результат для первого периода с учетом погрешности:</p><p>$T_1 = (0,63 \pm 0,02)$ с</p><p><strong>Ответ:</strong> Формула для расчёта периода: $T = \frac{t}{N}$. Значение периода для первого опыта: $T_1 = (0,63 \pm 0,02)$ с.</p><p><strong>Повторите опыт, увеличив амплитуду колебаний примерно в 2 раза. Запишите соответствующий промежуток времени t₂, вычислите период колебаний Т₂. Результат запишите с указанием погрешности в таблицу.</strong></p><p>Вычислим период для второго опыта, используя время $t_2 = 6,4$ с:</p><p>$T_2 = \frac{t_2}{N} = \frac{6,4 \text{ с}}{10} = 0,64 \text{ с}$</p><p>Погрешность измерения периода во втором опыте рассчитывается аналогично и имеет то же значение, так как условия измерения не изменились:</p><p>$\Delta T_2 = \frac{0,2 \text{ с}}{10} = 0,02 \text{ с}$</p><p>Результат для второго периода с учетом погрешности:</p><p>$T_2 = (0,64 \pm 0,02)$ с</p><p><strong>Ответ:</strong> Значение периода для второго опыта: $T_2 = (0,64 \pm 0,02)$ с.</p><p><strong>Сделайте вывод о зависимости или независимости периода колебаний пружинного маятника от амплитуды колебаний.</strong></p><p>Для вывода сравним полученные значения периодов: $T_1 = (0,63 \pm 0,02)$ с и $T_2 = (0,64 \pm 0,02)$ с. Разница между средними значениями периодов составляет $|T_2 - T_1| = |0,64 - 0,63| = 0,01$ с. Эта разница меньше, чем погрешность измерений каждого из периодов ($\Delta T = 0,02$ с). Это означает, что измеренные значения согласуются друг с другом в пределах погрешности. Проверим пересечение доверительных интервалов:</p><p>Интервал для $T_1$: $[0,63 - 0,02; 0,63 + 0,02] = [0,61\text{ с}; 0,65\text{ с}]$</p><p>Интервал для $T_2$: $[0,64 - 0,02; 0,64 + 0,02] = [0,62\text{ с}; 0,66\text{ с}]$</p><p>Поскольку интервалы возможных значений периодов пересекаются, можно сделать вывод, что период колебаний не изменился при увеличении амплитуды в 2 раза.</p><p><strong>Ответ:</strong> Период колебаний пружинного маятника в пределах погрешности измерений не зависит от амплитуды колебаний (при малых амплитудах).</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" => "1433923" "type" => "task" ] "previous" => array:2 [ "refs" => "1433921" "type" => "task" ] "book" => 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+timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1433922 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "201" "field_page_end" => "202" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/labrab7-1" "field_display_title" => "Задание 1" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1036} "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 {#1034} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1074} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1110} "content" => Illuminate\Database\Eloquent\Collection {#1072} "next" => array:2 [ "refs" => "1433923" "type" => "task" ] "previous" => array:2 [ "refs" => "1433921" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1105} "page" => array:2 [ "refs" => "1434600" "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 => "*" ] }
Задание 1 (с. 201)
Условие. Задание 1 (с. 201)
скриншот условия
7. Изучение колебаний пружинного маятника
Цель работы: исследовать зависимость периода колебаний груза на пружине от амплитуды колебаний, жёсткости пружины и массы груза; определить частоту колебаний груза.
Оборудование: штатив, две пружины различной жёсткости1), набор грузов по механике массой по 100 г, секундомер или часы с секундной стрелкой.
Ход работы
Задание 1. Исследование зависимости периода колебаний пружинного маятника от амплитуды.
• Подвесьте пружину к штативу, а к пружине подвесьте один груз. Отведите груз вниз от положения равновесия примерно на 1 см и отпустите. Измерьте промежуток времени $t_1$, за который совершается 10 полных колебаний. Результат запишите с указанием погрешности в таблицу (ниже приведён заголовок таблицы).
N | $t_1$, с | $T_1$, с | $t_2$, с | $T_2$, с
• Запишите формулу для расчёта периода колебаний $T_1$ и найдите значение периода. Запишите результат с указанием погрешности1) в таблицу.
• Повторите опыт, увеличив амплитуду колебаний примерно в 2 раза. Запишите соответствующий промежуток времени $t_2$, вычислите период колебаний $T_2$. Результат запишите с указанием погрешности в таблицу.
• Сделайте вывод о зависимости или независимости периода колебаний пружинного маятника от амплитуды колебаний.
Решение. Задание 1 (с. 201)
Дано:
Число полных колебаний: $N = 10$
Для проведения мысленного эксперимента возьмем следующие правдоподобные результаты измерений:
Время 10 колебаний при амплитуде $A_1 \approx 1$ см: $t_1 = 6,3$ с
Время 10 колебаний при амплитуде $A_2 \approx 2$ см: $t_2 = 6,4$ с
Абсолютная погрешность измерения времени секундомером (с учетом реакции экспериментатора): $\Delta t = 0,2$ с
Все данные представлены в системе СИ.
Найти:
1. Период колебаний $T_1$ и его погрешность $\Delta T_1$.
2. Период колебаний $T_2$ и его погрешность $\Delta T_2$.
3. Сделать вывод о зависимости периода колебаний от амплитуды.
Решение:
Результаты измерений и вычислений, полученные в ходе выполнения работы, сведены в таблицу:
| N | $t_1$, с | $T_1$, с | $t_2$, с | $T_2$, с |
|---|---|---|---|---|
| 10 | $6,3 \pm 0,2$ | $0,63 \pm 0,02$ | $6,4 \pm 0,2$ | $0,64 \pm 0,02$ |
Ниже представлены расчеты, на основе которых была заполнена таблица.
Запишите формулу для расчёта периода колебаний T₁ и найдите значение периода. Запишите результат с указанием погрешности¹) в таблицу.
Период колебаний $\text{T}$ – это время одного полного колебания. Для его нахождения необходимо общее время колебаний $\text{t}$ разделить на число совершенных за это время полных колебаний $\text{N}$.
Формула для расчёта периода:
$T = \frac{t}{N}$
Вычислим период для первого опыта:
$T_1 = \frac{t_1}{N} = \frac{6,3 \text{ с}}{10} = 0,63 \text{ с}$
Абсолютная погрешность измерения периода вычисляется по формуле $\Delta T = \frac{\Delta t}{N}$, так как число колебаний $\text{N}$ является точной величиной.
$\Delta T_1 = \frac{0,2 \text{ с}}{10} = 0,02 \text{ с}$
Таким образом, результат для первого периода с учетом погрешности:
$T_1 = (0,63 \pm 0,02)$ с
Ответ: Формула для расчёта периода: $T = \frac{t}{N}$. Значение периода для первого опыта: $T_1 = (0,63 \pm 0,02)$ с.
Повторите опыт, увеличив амплитуду колебаний примерно в 2 раза. Запишите соответствующий промежуток времени t₂, вычислите период колебаний Т₂. Результат запишите с указанием погрешности в таблицу.
Вычислим период для второго опыта, используя время $t_2 = 6,4$ с:
$T_2 = \frac{t_2}{N} = \frac{6,4 \text{ с}}{10} = 0,64 \text{ с}$
Погрешность измерения периода во втором опыте рассчитывается аналогично и имеет то же значение, так как условия измерения не изменились:
$\Delta T_2 = \frac{0,2 \text{ с}}{10} = 0,02 \text{ с}$
Результат для второго периода с учетом погрешности:
$T_2 = (0,64 \pm 0,02)$ с
Ответ: Значение периода для второго опыта: $T_2 = (0,64 \pm 0,02)$ с.
Сделайте вывод о зависимости или независимости периода колебаний пружинного маятника от амплитуды колебаний.
Для вывода сравним полученные значения периодов: $T_1 = (0,63 \pm 0,02)$ с и $T_2 = (0,64 \pm 0,02)$ с. Разница между средними значениями периодов составляет $|T_2 - T_1| = |0,64 - 0,63| = 0,01$ с. Эта разница меньше, чем погрешность измерений каждого из периодов ($\Delta T = 0,02$ с). Это означает, что измеренные значения согласуются друг с другом в пределах погрешности. Проверим пересечение доверительных интервалов:
Интервал для $T_1$: $[0,63 - 0,02; 0,63 + 0,02] = [0,61\text{ с}; 0,65\text{ с}]$
Интервал для $T_2$: $[0,64 - 0,02; 0,64 + 0,02] = [0,62\text{ с}; 0,66\text{ с}]$
Поскольку интервалы возможных значений периодов пересекаются, можно сделать вывод, что период колебаний не изменился при увеличении амплитуды в 2 раза.
Ответ: Период колебаний пружинного маятника в пределах погрешности измерений не зависит от амплитуды колебаний (при малых амплитудах).
Другие задания:
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