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Номер 2.20, страница 12 - гдз по физике 9 класс задачник Артеменков, Ломаченков
Авторы: Артеменков Д. А., Ломаченков И. А., Панебратцев Ю. А.
Тип: Задачник
Серия: сферы
Издательство: Просвещение
Год издания: 2011 - 2026
Цвет обложки: синий
ISBN: 978-5-09-038216-8
Популярные ГДЗ в 9 классе
II. Механические колебания и волны - номер 2.20, страница 12.
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" => 1424134 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "12" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-20" "field_display_title" => "2.20" "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" => 1424065 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "II. Механические колебания и волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "10" "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 {#1081 #items: array:1 [ 0 => App\Models\Book {#1048 #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" => 2549 "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 {#1050 #items: array:1 [ 0 => App\Models\Term {#1049 #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 {#1051 #items: array:1 [ 0 => App\Models\Term {#1052 #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 {#1053 #items: array:1 [ 0 => App\Models\Term {#1054 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1055 #items: array:3 [ 0 => App\Models\Term {#1056 #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" => 3745 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Артеменков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Денис" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 3745 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Артеменков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Денис" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => 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" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "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 {#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" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #original: array:12 [ "id" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #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" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #original: array:10 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #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: array:1 [ 0 => App\Models\Term {#1067 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #original: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Term {#1072 #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" => 37 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное и дополненное" "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" => "pererabotannoe i dopolnennoe" ] #original: array:6 [ "id" => 37 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное и дополненное" "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" => "pererabotannoe i dopolnennoe" ] #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 {#1073 #items: array:1 [ 0 => App\Models\Term {#1058} ] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "278" "field_priority" => null "field_default_folder" => "/fizika_09/artemenkov-z/" "field_isbn" => "978-5-09-038216-8" "field_cover" => array:1 [ 0 => "/media/fizika_09/artemenkov-z/covers/cover1.webp?ts=1758483621" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/artemenkov-z/covers/cover1.webp?ts=1758483621" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ 0 => App\Models\Term {#1078 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "siniy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 2549 "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 {#1050} "field_class" => Illuminate\Database\Eloquent\Collection {#1051} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1053} "field_author" => Illuminate\Database\Eloquent\Collection {#1055} "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 {#1068} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1069} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1070} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1071} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1073} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "278" "field_priority" => null "field_default_folder" => "/fizika_09/artemenkov-z/" "field_isbn" => "978-5-09-038216-8" "field_cover" => array:1 [ 0 => "/media/fizika_09/artemenkov-z/covers/cover1.webp?ts=1758483621" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/artemenkov-z/covers/cover1.webp?ts=1758483621" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1074} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1075} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1076} "field_url" => "/9-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1077} "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 {#1079 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1424065 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "II. Механические колебания и волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047} "field_page_start" => "10" "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 {#1081} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1079} ] #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 {#1038 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1034 #items: array:2 [ 0 => App\Models\Element {#1085 #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" => 1673752 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1094 #items: array:1 [ 0 => App\Models\Edition {#1086 #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" => 5990 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1088 #items: array:1 [ 0 => App\Models\Term {#1087 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_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 {#1089 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1090 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1091 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5990 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1088} "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 {#1089} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1090} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1091} "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" => "1424134" "type" => "task" ] "text" => "<p><strong>2.20</strong> Определите массу груза пружинного маятника, если он делает 45 колебаний за 30 с, а жёсткость пружины равна 40 Н/м.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "20-1.jpg" "alt" => null "width" => "1721" "height" => 219 "path" => "/media/fizika_09/artemenkov-z/0-2/20-1.webp?ts=1758726373" ] ] ] #original: array:7 [ "id" => 1673752 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1094} "task" => array:2 [ "refs" => "1424134" "type" => "task" ] "text" => "<p><strong>2.20</strong> Определите массу груза пружинного маятника, если он делает 45 колебаний за 30 с, а жёсткость пружины равна 40 Н/м.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "20-1.jpg" "alt" => null "width" => "1721" "height" => 219 "path" => "/media/fizika_09/artemenkov-z/0-2/20-1.webp?ts=1758726373" ] ] ] #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" => 1695294 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1102 #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" => 6166 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:1 [ 0 => App\Models\Term {#1095 #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 …4 ] "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 [ …6] "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 {#1097 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1098 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1099 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6166 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096} "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 {#1097} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1098} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1099} "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" => "1424134" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Число колебаний, $N = 45$</p><p>Время колебаний, $t = 30$ с</p><p>Жёсткость пружины, $k = 40$ Н/м</p><p><strong>Найти:</strong></p><p>Массу груза, $m$</p><p><strong>Решение:</strong></p><p>Период колебаний пружинного маятника определяется по формуле:</p><p>$T = 2\pi\sqrt{\frac{m}{k}}$</p><p>где $T$ - период колебаний, $m$ - масса груза, а $k$ - жёсткость пружины.</p><p>С другой стороны, период колебаний можно рассчитать, зная общее время колебаний $t$ и число полных колебаний $N$ за это время:</p><p>$T = \frac{t}{N}$</p><p>Так как левые части обоих уравнений равны, мы можем приравнять их правые части:</p><p>$2\pi\sqrt{\frac{m}{k}} = \frac{t}{N}$</p><p>Для того чтобы выразить массу $m$, возведём обе части уравнения в квадрат:</p><p>$(2\pi\sqrt{\frac{m}{k}})^2 = (\frac{t}{N})^2$</p><p>$4\pi^2 \frac{m}{k} = \frac{t^2}{N^2}$</p><p>Из этого уравнения выразим массу $m$:</p><p>$m = \frac{k \cdot t^2}{4\pi^2 \cdot N^2}$</p><p>Теперь подставим известные числовые значения в полученную формулу:</p><p>$m = \frac{40 \text{ Н/м} \cdot (30 \text{ с})^2}{4\pi^2 \cdot (45)^2} = \frac{40 \cdot 900}{4\pi^2 \cdot 2025} = \frac{36000}{8100\pi^2} = \frac{40}{9\pi^2}$ кг</p><p>Вычислим приближённое значение массы, приняв $\pi \approx 3.14$:</p><p>$m \approx \frac{40}{9 \cdot (3.14)^2} \approx \frac{40}{9 \cdot 9.8596} \approx \frac{40}{88.7364} \approx 0.4507$ кг</p><p>Округлим результат до двух значащих цифр.</p><p><strong>Ответ:</strong> масса груза пружинного маятника составляет примерно 0,45 кг.</p>" ] #original: array:6 [ "id" => 1695294 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1102} "task" => array:2 [ "refs" => "1424134" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Число колебаний, $N = 45$</p><p>Время колебаний, $t = 30$ с</p><p>Жёсткость пружины, $k = 40$ Н/м</p><p><strong>Найти:</strong></p><p>Массу груза, $m$</p><p><strong>Решение:</strong></p><p>Период колебаний пружинного маятника определяется по формуле:</p><p>$T = 2\pi\sqrt{\frac{m}{k}}$</p><p>где $T$ - период колебаний, $m$ - масса груза, а $k$ - жёсткость пружины.</p><p>С другой стороны, период колебаний можно рассчитать, зная общее время колебаний $t$ и число полных колебаний $N$ за это время:</p><p>$T = \frac{t}{N}$</p><p>Так как левые части обоих уравнений равны, мы можем приравнять их правые части:</p><p>$2\pi\sqrt{\frac{m}{k}} = \frac{t}{N}$</p><p>Для того чтобы выразить массу $m$, возведём обе части уравнения в квадрат:</p><p>$(2\pi\sqrt{\frac{m}{k}})^2 = (\frac{t}{N})^2$</p><p>$4\pi^2 \frac{m}{k} = \frac{t^2}{N^2}$</p><p>Из этого уравнения выразим массу $m$:</p><p>$m = \frac{k \cdot t^2}{4\pi^2 \cdot N^2}$</p><p>Теперь подставим известные числовые значения в полученную формулу:</p><p>$m = \frac{40 \text{ Н/м} \cdot (30 \text{ с})^2}{4\pi^2 \cdot (45)^2} = \frac{40 \cdot 900}{4\pi^2 \cdot 2025} = \frac{36000}{8100\pi^2} = \frac{40}{9\pi^2}$ кг</p><p>Вычислим приближённое значение массы, приняв $\pi \approx 3.14$:</p><p>$m \approx \frac{40}{9 \cdot (3.14)^2} \approx \frac{40}{9 \cdot 9.8596} \approx \frac{40}{88.7364} \approx 0.4507$ кг</p><p>Округлим результат до двух значащих цифр.</p><p><strong>Ответ:</strong> масса груза пружинного маятника составляет примерно 0,45 кг.</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" => "1424135" "type" => "task" ] "previous" => array:2 [ "refs" => "1424133" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1082 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\BookPage {#1080 #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" => 1424362 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "12" "field_url" => "/9-klass/fizika/artemenkov-zadachnik/page-12" "field_display_title" => "12" "field_folder" => "1" "field_image_name" => "12" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1100 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1101 #items: array:1 [ 0 => App\Models\Book {#1048} ] #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 {#1103 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1113 #items: array:1 [ 0 => App\Models\Element {#1112 #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" => 1674172 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1114 #items: array:1 [ 0 => App\Models\Edition {#1086} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1424362" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "12-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_09/artemenkov-z/0-1/12-1.webp?ts=1758727968" ] ] ] #original: array:6 [ "id" => 1674172 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1114} "book_page" => array:2 [ "refs" => "1424362" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "12-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_09/artemenkov-z/0-1/12-1.webp?ts=1758727968" ] ] ] #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" => "1424363" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1424361" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1168 #items: array:5 [ 0 => App\Models\Task {#1180 #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" => 1424132 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "12" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-18" "field_display_title" => "2.18" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1181 #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 {#1182 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1183 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1184 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1186 #items: array:2 [ 0 => App\Models\Element {#1195 #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" => 1673750 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1196 …2} "task" => array:2 [ …2] "text" => "<p><strong>2.18</strong> Груз, колеблющийся на пружине, за 16 с совершает 64 колебания. Определите период и частоту колебаний.</p>" "img" => array:1 [ …1] ] #original: array:7 [ "id" => 1673750 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1196 …2} "task" => array:2 [ …2] "text" => "<p><strong>2.18</strong> Груз, колеблющийся на пружине, за 16 с совершает 64 колебания. Определите период и частоту колебаний.</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 {#1197 #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" => 1695292 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1198 …2} "task" => array:2 [ …2] "text" => "<p><strong>Дано</strong></p><p>Время колебаний: $t = 16$ с</p><p>Число колебаний: $N = 64$</p><p><strong>Найти:</strong></p><p>Период колебаний: $T$ - ?</p><p>Частота колебаний: $\nu$ - ?</p><p><strong>Решение</strong></p><p>Период колебаний ($T$) — это время, за которое совершается одно полное колебание. Чтобы найти период, нужно общее время колебаний ($t$) разделить на число колебаний ($N$), совершенных за это время.</p><p>Формула для расчета периода:</p><p>$T = \frac{t}{N}$</p><p>Подставим данные из условия задачи в формулу:</p><p>$T = \frac{16 \text{ с}}{64} = 0.25 \text{ с}$</p><p>Частота колебаний ($\nu$) — это число полных колебаний, совершаемых за единицу времени. Чтобы найти частоту, нужно число колебаний ($N$) разделить на время ($t$), в течение которого они происходили.</p><p>Формула для расчета частоты:</p><p>$\nu = \frac{N}{t}$</p><p>Подставим данные из условия задачи в формулу:</p><p>$\nu = \frac{64}{16 \text{ с}} = 4 \text{ с}^{-1} = 4 \text{ Гц}$</p><p>Частота и период являются взаимно обратными величинами, поэтому можно проверить правильность расчетов:</p><p>$\nu = \frac{1}{T} = \frac{1}{0.25 \text{ с}} = 4 \text{ Гц}$</p><p>Расчеты верны.</p><p><strong>Ответ:</strong> период колебаний $T = 0.25$ с, частота колебаний $\nu = 4$ Гц.</p>" ] #original: array:6 [ "id" => 1695292 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1198 …2} "task" => array:2 [ …2] "text" => "<p><strong>Дано</strong></p><p>Время колебаний: $t = 16$ с</p><p>Число колебаний: $N = 64$</p><p><strong>Найти:</strong></p><p>Период колебаний: $T$ - ?</p><p>Частота колебаний: $\nu$ - ?</p><p><strong>Решение</strong></p><p>Период колебаний ($T$) — это время, за которое совершается одно полное колебание. Чтобы найти период, нужно общее время колебаний ($t$) разделить на число колебаний ($N$), совершенных за это время.</p><p>Формула для расчета периода:</p><p>$T = \frac{t}{N}$</p><p>Подставим данные из условия задачи в формулу:</p><p>$T = \frac{16 \text{ с}}{64} = 0.25 \text{ с}$</p><p>Частота колебаний ($\nu$) — это число полных колебаний, совершаемых за единицу времени. Чтобы найти частоту, нужно число колебаний ($N$) разделить на время ($t$), в течение которого они происходили.</p><p>Формула для расчета частоты:</p><p>$\nu = \frac{N}{t}$</p><p>Подставим данные из условия задачи в формулу:</p><p>$\nu = \frac{64}{16 \text{ с}} = 4 \text{ с}^{-1} = 4 \text{ Гц}$</p><p>Частота и период являются взаимно обратными величинами, поэтому можно проверить правильность расчетов:</p><p>$\nu = \frac{1}{T} = \frac{1}{0.25 \text{ с}} = 4 \text{ Гц}$</p><p>Расчеты верны.</p><p><strong>Ответ:</strong> период колебаний $T = 0.25$ с, частота колебаний $\nu = 4$ Гц.</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" => "1424133" "type" => "task" ] "previous" => array:2 [ "refs" => "1424131" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1192 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424362" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424132 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "12" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-18" "field_display_title" => "2.18" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1181} "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 {#1182} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1183} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1184} "content" => Illuminate\Database\Eloquent\Collection {#1186} "next" => array:2 [ "refs" => "1424133" "type" => "task" ] "previous" => array:2 [ "refs" => "1424131" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1192} "page" => array:2 [ "refs" => "1424362" "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 {#1187 #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" => 1424133 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "12" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-19" "field_display_title" => "2.19" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1185 #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 {#1194 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1190 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1188 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1189 #items: array:2 [ 0 => App\Models\Element {#1207 #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" => 1673751 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1208 …2} "task" => array:2 [ …2] "text" => "<p><strong>2.19</strong> Определите период колебаний пружинного маятника, если масса груза равна 250 г, а жёсткость пружины 100 Н/м.</p>" "img" => array:1 [ …1] ] #original: array:7 [ "id" => 1673751 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1208 …2} "task" => array:2 [ …2] "text" => "<p><strong>2.19</strong> Определите период колебаний пружинного маятника, если масса груза равна 250 г, а жёсткость пружины 100 Н/м.</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 {#1209 #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" => 1695293 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1210 …2} "task" => array:2 [ …2] "text" => "<p><strong>Дано:</strong></p><p>$m = 250$ г</p><p>$k = 100$ Н/м</p><p><em>Перевод в систему СИ:</em></p><p>$m = 250 \text{ г} = 0.25 \text{ кг}$</p><p><strong>Найти:</strong></p><p>$T$ - ?</p><p><strong>Решение:</strong></p><p>Период колебаний пружинного маятника ($T$) определяется по формуле:</p><p>$T = 2\pi \sqrt{\frac{m}{k}}$</p><p>где $m$ — масса груза, прикрепленного к пружине, а $k$ — жёсткость пружины.</p><p>Подставим в формулу значения величин в системе СИ:</p><p>$T = 2\pi \sqrt{\frac{0.25 \text{ кг}}{100 \text{ Н/м}}}$</p><p>Выполним вычисления под корнем:</p><p>$\frac{0.25}{100} = 0.0025$</p><p>Теперь извлечем квадратный корень:</p><p>$\sqrt{0.0025} = 0.05$</p><p>Подставим полученное значение обратно в формулу для периода:</p><p>$T = 2\pi \cdot 0.05 \text{ с} = 0.1\pi \text{ с}$</p><p>Для получения конечного численного ответа используем приближенное значение числа $\pi \approx 3.14$:</p><p>$T \approx 0.1 \cdot 3.14 \text{ с} = 0.314 \text{ с}$</p><p><strong>Ответ:</strong> период колебаний пружинного маятника составляет примерно $0.314$ с.</p>" ] #original: array:6 [ "id" => 1695293 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1210 …2} "task" => array:2 [ …2] "text" => "<p><strong>Дано:</strong></p><p>$m = 250$ г</p><p>$k = 100$ Н/м</p><p><em>Перевод в систему СИ:</em></p><p>$m = 250 \text{ г} = 0.25 \text{ кг}$</p><p><strong>Найти:</strong></p><p>$T$ - ?</p><p><strong>Решение:</strong></p><p>Период колебаний пружинного маятника ($T$) определяется по формуле:</p><p>$T = 2\pi \sqrt{\frac{m}{k}}$</p><p>где $m$ — масса груза, прикрепленного к пружине, а $k$ — жёсткость пружины.</p><p>Подставим в формулу значения величин в системе СИ:</p><p>$T = 2\pi \sqrt{\frac{0.25 \text{ кг}}{100 \text{ Н/м}}}$</p><p>Выполним вычисления под корнем:</p><p>$\frac{0.25}{100} = 0.0025$</p><p>Теперь извлечем квадратный корень:</p><p>$\sqrt{0.0025} = 0.05$</p><p>Подставим полученное значение обратно в формулу для периода:</p><p>$T = 2\pi \cdot 0.05 \text{ с} = 0.1\pi \text{ с}$</p><p>Для получения конечного численного ответа используем приближенное значение числа $\pi \approx 3.14$:</p><p>$T \approx 0.1 \cdot 3.14 \text{ с} = 0.314 \text{ с}$</p><p><strong>Ответ:</strong> период колебаний пружинного маятника составляет примерно $0.314$ с.</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" => "1424134" "type" => "task" ] "previous" => array:2 [ "refs" => "1424132" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1204 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424362" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424133 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "12" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-19" "field_display_title" => "2.19" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1185} "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 {#1194} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1190} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1188} "content" => Illuminate\Database\Eloquent\Collection {#1189} "next" => array:2 [ "refs" => "1424134" "type" => "task" ] "previous" => array:2 [ "refs" => "1424132" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1204} "page" => array:2 [ "refs" => "1424362" "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 {#1199 #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" => 1424134 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "12" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-20" "field_display_title" => "2.20" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1191 #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 {#1206 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1202 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1200 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1203 #items: array:2 [ 0 => App\Models\Element {#1085} 1 => App\Models\Element {#1092} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1424135" "type" => "task" ] "previous" => array:2 [ "refs" => "1424133" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1201 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424362" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424134 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "12" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-20" "field_display_title" => "2.20" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1191} "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 {#1206} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1202} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1200} "content" => Illuminate\Database\Eloquent\Collection {#1203} "next" => array:2 [ "refs" => "1424135" "type" => "task" ] "previous" => array:2 [ "refs" => "1424133" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1201} "page" => array:2 [ "refs" => "1424362" "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 {#1211 #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" => 1424135 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "12" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-21" "field_display_title" => "2.21" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1212 #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 {#1213 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1214 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1215 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1217 #items: array:2 [ 0 => App\Models\Element {#1226 #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" => 1673753 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1227 …2} "task" => array:2 [ …2] "text" => "<p><strong>2.21</strong> Сравните амплитуды, периоды, частоты колебательных процессов, графики которых приведены на рисунке 2.</p><p>Рис. 2</p>" "img" => array:1 [ …1] ] #original: array:7 [ "id" => 1673753 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1227 …2} "task" => array:2 [ …2] "text" => "<p><strong>2.21</strong> Сравните амплитуды, периоды, частоты колебательных процессов, графики которых приведены на рисунке 2.</p><p>Рис. 2</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 {#1228 #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" => 1695295 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1229 …2} "task" => array:2 [ …2] "text" => "<p><strong>Дано:</strong></p><p>Графики зависимости смещения от времени $x(t)$ для двух колебательных процессов.</p><p><strong>Найти:</strong></p><p>Сравнить амплитуды ($A_1, A_2$), периоды ($T_1, T_2$) и частоты ($f_1, f_2$) колебательных процессов.</p><p><strong>Решение:</strong></p><p>Для сравнения характеристик колебательных процессов сначала определим их значения по графикам.</p><p><strong>Амплитуды</strong></p><p>Амплитуда — это максимальное смещение от положения равновесия.</p><p>По первому графику (вверху) максимальное смещение $x_{1,max} = 75 \text{ см}$. Амплитуда $A_1 = 75 \text{ см} = 0,75 \text{ м}$.</p><p>По второму графику (внизу) максимальное смещение $x_{2,max} = 5 \text{ м}$. Амплитуда $A_2 = 5 \text{ м}$.</p><p>Сравним значения: $A_2 > A_1$, так как $5 \text{ м} > 0,75 \text{ м}$.</p><p>Найдем отношение амплитуд: $\frac{A_2}{A_1} = \frac{5 \text{ м}}{0,75 \text{ м}} \approx 6,7$.</p><p><strong>Ответ:</strong> Амплитуда второго колебания больше амплитуды первого примерно в 6,7 раз.</p><p><strong>Периоды</strong></p><p>Период — это время одного полного колебания.</p><p>По первому графику определяем период, например, по времени между двумя последовательными максимумами в $t=2 \text{ с}$ и $t=10 \text{ с}$: $T_1 = 10 \text{ с} - 2 \text{ с} = 8 \text{ с}$.</p><p>По второму графику одно полное колебание происходит за время $T_2 = 0,5 \text{ с}$ (например, от $t=0$ до $t=0,5 \text{ с}$).</p><p>Сравниваем значения: $T_1 > T_2$, так как $8 \text{ с} > 0,5 \text{ с}$.</p><p>Найдем отношение периодов: $\frac{T_1}{T_2} = \frac{8 \text{ с}}{0,5 \text{ с}} = 16$.</p><p><strong>Ответ:</strong> Период первого колебания больше периода второго в 16 раз.</p><p><strong>Частоты</strong></p><p>Частота колебаний — это величина, обратная периоду ($f = \frac{1}{T}$).</p><p>Частота первого процесса: $f_1 = \frac{1}{T_1} = \frac{1}{8 \text{ с}} = 0,125 \text{ Гц}$.</p><p>Частота второго процесса: $f_2 = \frac{1}{T_2} = \frac{1}{0,5 \text{ с}} = 2 \text{ Гц}$.</p><p>Сравниваем значения: $f_2 > f_1$, так как $2 \text{ Гц} > 0,125 \text{ Гц}$.</p><p>Найдем отношение частот: $\frac{f_2}{f_1} = \frac{2 \text{ Гц}}{0,125 \text{ Гц}} = 16$.</p><p><strong>Ответ:</strong> Частота второго колебания больше частоты первого в 16 раз.</p>" ] #original: array:6 [ "id" => 1695295 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1229 …2} "task" => array:2 [ …2] "text" => "<p><strong>Дано:</strong></p><p>Графики зависимости смещения от времени $x(t)$ для двух колебательных процессов.</p><p><strong>Найти:</strong></p><p>Сравнить амплитуды ($A_1, A_2$), периоды ($T_1, T_2$) и частоты ($f_1, f_2$) колебательных процессов.</p><p><strong>Решение:</strong></p><p>Для сравнения характеристик колебательных процессов сначала определим их значения по графикам.</p><p><strong>Амплитуды</strong></p><p>Амплитуда — это максимальное смещение от положения равновесия.</p><p>По первому графику (вверху) максимальное смещение $x_{1,max} = 75 \text{ см}$. Амплитуда $A_1 = 75 \text{ см} = 0,75 \text{ м}$.</p><p>По второму графику (внизу) максимальное смещение $x_{2,max} = 5 \text{ м}$. Амплитуда $A_2 = 5 \text{ м}$.</p><p>Сравним значения: $A_2 > A_1$, так как $5 \text{ м} > 0,75 \text{ м}$.</p><p>Найдем отношение амплитуд: $\frac{A_2}{A_1} = \frac{5 \text{ м}}{0,75 \text{ м}} \approx 6,7$.</p><p><strong>Ответ:</strong> Амплитуда второго колебания больше амплитуды первого примерно в 6,7 раз.</p><p><strong>Периоды</strong></p><p>Период — это время одного полного колебания.</p><p>По первому графику определяем период, например, по времени между двумя последовательными максимумами в $t=2 \text{ с}$ и $t=10 \text{ с}$: $T_1 = 10 \text{ с} - 2 \text{ с} = 8 \text{ с}$.</p><p>По второму графику одно полное колебание происходит за время $T_2 = 0,5 \text{ с}$ (например, от $t=0$ до $t=0,5 \text{ с}$).</p><p>Сравниваем значения: $T_1 > T_2$, так как $8 \text{ с} > 0,5 \text{ с}$.</p><p>Найдем отношение периодов: $\frac{T_1}{T_2} = \frac{8 \text{ с}}{0,5 \text{ с}} = 16$.</p><p><strong>Ответ:</strong> Период первого колебания больше периода второго в 16 раз.</p><p><strong>Частоты</strong></p><p>Частота колебаний — это величина, обратная периоду ($f = \frac{1}{T}$).</p><p>Частота первого процесса: $f_1 = \frac{1}{T_1} = \frac{1}{8 \text{ с}} = 0,125 \text{ Гц}$.</p><p>Частота второго процесса: $f_2 = \frac{1}{T_2} = \frac{1}{0,5 \text{ с}} = 2 \text{ Гц}$.</p><p>Сравниваем значения: $f_2 > f_1$, так как $2 \text{ Гц} > 0,125 \text{ Гц}$.</p><p>Найдем отношение частот: $\frac{f_2}{f_1} = \frac{2 \text{ Гц}}{0,125 \text{ Гц}} = 16$.</p><p><strong>Ответ:</strong> Частота второго колебания больше частоты первого в 16 раз.</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" => "1424136" "type" => "task" ] "previous" => array:2 [ "refs" => "1424134" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1223 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424362" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424135 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "12" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-21" "field_display_title" => "2.21" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1212} "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 {#1213} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1214} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1215} "content" => Illuminate\Database\Eloquent\Collection {#1217} "next" => array:2 [ "refs" => "1424136" "type" => "task" ] "previous" => array:2 [ "refs" => "1424134" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1223} "page" => array:2 [ "refs" => "1424362" "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 => "*" ] } 4 => App\Models\Task {#1218 #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" => 1424136 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "12" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-22" "field_display_title" => "2.22" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1216 #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 {#1225 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1221 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1219 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1220 #items: array:2 [ 0 => App\Models\Element {#1238 #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" => 1673754 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1239 …2} "task" => array:2 [ …2] "text" => "<p><strong>2.22</strong> На рисунке 3 приведён график колебательного движения груза на пружине. Определите координату груза в моменты времени: $t=0$, $t=1$ с, $t=2,5$ с, $t=4$ с. Определите амплитуду, период и частоту колебаний груза.</p><p>Рис. 3</p>" "img" => array:1 [ …1] ] #original: array:7 [ "id" => 1673754 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1239 …2} "task" => array:2 [ …2] "text" => "<p><strong>2.22</strong> На рисунке 3 приведён график колебательного движения груза на пружине. Определите координату груза в моменты времени: $t=0$, $t=1$ с, $t=2,5$ с, $t=4$ с. Определите амплитуду, период и частоту колебаний груза.</p><p>Рис. 3</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 {#1240 #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" => 1695296 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1241 …2} "task" => array:2 [ …2] "text" => "<p><strong>Дано:</strong></p><p>График колебательного движения груза $x(t)$.</p><p><strong>Найти:</strong></p><p><strong>1.</strong> Координату груза в моменты времени $t=0$; $t=1$ с; $t=2,5$ с; $t=4$ с.</p><p><strong>2.</strong> Амплитуду колебаний $A$.</p><p><strong>3.</strong> Период колебаний $T$.</p><p><strong>4.</strong> Частоту колебаний $\nu$.</p><p><strong>Решение:</strong></p><p><strong>Координата груза в моменты времени: t=0, t=1 c, t=2,5 c, t=4 c</strong></p><p>Для определения координаты груза в указанные моменты времени воспользуемся представленным графиком зависимости координаты от времени $x(t)$.</p><p>При $t=0$ с, из графика находим, что координата $x = 32$ мм.</p><p>При $t=1$ с, из графика находим, что координата $x = -32$ мм.</p><p>При $t=2,5$ с, график пересекает ось времени, следовательно, координата груза $x = 0$ мм.</p><p>При $t=4$ с, из графика находим, что координата груза снова равна $x = 32$ мм.</p><p><strong>Ответ:</strong> $x(0) = 32$ мм; $x(1) = -32$ мм; $x(2,5) = 0$ мм; $x(4) = 32$ мм.</p><p><strong>Амплитуда колебаний</strong></p><p>Амплитуда $A$ — это модуль максимального смещения тела от положения равновесия. По графику видно, что максимальное отклонение от положения равновесия ($x=0$) составляет 32 мм.</p><p>$A = 32$ мм.</p><p>В системе СИ: $A = 32 \cdot 10^{-3}$ м $= 0,032$ м.</p><p><strong>Ответ:</strong> $A = 32$ мм (или 0,032 м).</p><p><strong>Период колебаний</strong></p><p>Период $T$ — это время одного полного колебания. Его можно определить по графику как промежуток времени между двумя последовательными точками, в которых состояние системы повторяется. Например, между двумя максимумами. Первый максимум наблюдается при $t=0$ с, а следующий — при $t=2$ с.</p><p>$T = 2 \text{ с} - 0 \text{ с} = 2$ с.</p><p><strong>Ответ:</strong> $T = 2$ с.</p><p><strong>Частота колебаний</strong></p><p>Частота колебаний $\nu$ — это число полных колебаний в единицу времени. Она является величиной, обратной периоду:</p><p>$\nu = \frac{1}{T}$</p><p>Подставляя найденное значение периода $T=2$ с, получаем:</p><p>$\nu = \frac{1}{2 \text{ с}} = 0,5$ Гц.</p><p><strong>Ответ:</strong> $\nu = 0,5$ Гц.</p>" ] #original: array:6 [ "id" => 1695296 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1241 …2} "task" => array:2 [ …2] "text" => "<p><strong>Дано:</strong></p><p>График колебательного движения груза $x(t)$.</p><p><strong>Найти:</strong></p><p><strong>1.</strong> Координату груза в моменты времени $t=0$; $t=1$ с; $t=2,5$ с; $t=4$ с.</p><p><strong>2.</strong> Амплитуду колебаний $A$.</p><p><strong>3.</strong> Период колебаний $T$.</p><p><strong>4.</strong> Частоту колебаний $\nu$.</p><p><strong>Решение:</strong></p><p><strong>Координата груза в моменты времени: t=0, t=1 c, t=2,5 c, t=4 c</strong></p><p>Для определения координаты груза в указанные моменты времени воспользуемся представленным графиком зависимости координаты от времени $x(t)$.</p><p>При $t=0$ с, из графика находим, что координата $x = 32$ мм.</p><p>При $t=1$ с, из графика находим, что координата $x = -32$ мм.</p><p>При $t=2,5$ с, график пересекает ось времени, следовательно, координата груза $x = 0$ мм.</p><p>При $t=4$ с, из графика находим, что координата груза снова равна $x = 32$ мм.</p><p><strong>Ответ:</strong> $x(0) = 32$ мм; $x(1) = -32$ мм; $x(2,5) = 0$ мм; $x(4) = 32$ мм.</p><p><strong>Амплитуда колебаний</strong></p><p>Амплитуда $A$ — это модуль максимального смещения тела от положения равновесия. По графику видно, что максимальное отклонение от положения равновесия ($x=0$) составляет 32 мм.</p><p>$A = 32$ мм.</p><p>В системе СИ: $A = 32 \cdot 10^{-3}$ м $= 0,032$ м.</p><p><strong>Ответ:</strong> $A = 32$ мм (или 0,032 м).</p><p><strong>Период колебаний</strong></p><p>Период $T$ — это время одного полного колебания. Его можно определить по графику как промежуток времени между двумя последовательными точками, в которых состояние системы повторяется. Например, между двумя максимумами. Первый максимум наблюдается при $t=0$ с, а следующий — при $t=2$ с.</p><p>$T = 2 \text{ с} - 0 \text{ с} = 2$ с.</p><p><strong>Ответ:</strong> $T = 2$ с.</p><p><strong>Частота колебаний</strong></p><p>Частота колебаний $\nu$ — это число полных колебаний в единицу времени. Она является величиной, обратной периоду:</p><p>$\nu = \frac{1}{T}$</p><p>Подставляя найденное значение периода $T=2$ с, получаем:</p><p>$\nu = \frac{1}{2 \text{ с}} = 0,5$ Гц.</p><p><strong>Ответ:</strong> $\nu = 0,5$ Гц.</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" => "1424137" "type" => "task" ] "previous" => array:2 [ "refs" => "1424135" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1235 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424362" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424136 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "12" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-22" "field_display_title" => "2.22" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1216} "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 {#1225} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1221} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1219} "content" => Illuminate\Database\Eloquent\Collection {#1220} "next" => array:2 [ "refs" => "1424137" "type" => "task" ] "previous" => array:2 [ "refs" => "1424135" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1235} "page" => array:2 [ "refs" => "1424362" "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" => 1424362 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "12" "field_url" => "/9-klass/fizika/artemenkov-zadachnik/page-12" "field_display_title" => "12" "field_folder" => "1" "field_image_name" => "12" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1100} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1101} "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 {#1103} "content" => Illuminate\Database\Eloquent\Collection {#1113} "next" => array:2 [ "refs" => "1424363" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1424361" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1168} ] #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" => 1424134 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "12" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-20" "field_display_title" => "2.20" "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 {#1038} "content" => Illuminate\Database\Eloquent\Collection {#1034} "next" => array:2 [ "refs" => "1424135" "type" => "task" ] "previous" => array:2 [ "refs" => "1424133" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1082} "page" => array:2 [ "refs" => "1424362" "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 => "*" ] }
№2.20 (с. 12)
Условие. №2.20 (с. 12)
скриншот условия
2.20 Определите массу груза пружинного маятника, если он делает 45 колебаний за 30 с, а жёсткость пружины равна 40 Н/м.
Решение. №2.20 (с. 12)
Дано:
Число колебаний, $N = 45$
Время колебаний, $t = 30$ с
Жёсткость пружины, $k = 40$ Н/м
Найти:
Массу груза, $m$
Решение:
Период колебаний пружинного маятника определяется по формуле:
$T = 2\pi\sqrt{\frac{m}{k}}$
где $T$ - период колебаний, $m$ - масса груза, а $k$ - жёсткость пружины.
С другой стороны, период колебаний можно рассчитать, зная общее время колебаний $t$ и число полных колебаний $N$ за это время:
$T = \frac{t}{N}$
Так как левые части обоих уравнений равны, мы можем приравнять их правые части:
$2\pi\sqrt{\frac{m}{k}} = \frac{t}{N}$
Для того чтобы выразить массу $m$, возведём обе части уравнения в квадрат:
$(2\pi\sqrt{\frac{m}{k}})^2 = (\frac{t}{N})^2$
$4\pi^2 \frac{m}{k} = \frac{t^2}{N^2}$
Из этого уравнения выразим массу $m$:
$m = \frac{k \cdot t^2}{4\pi^2 \cdot N^2}$
Теперь подставим известные числовые значения в полученную формулу:
$m = \frac{40 \text{ Н/м} \cdot (30 \text{ с})^2}{4\pi^2 \cdot (45)^2} = \frac{40 \cdot 900}{4\pi^2 \cdot 2025} = \frac{36000}{8100\pi^2} = \frac{40}{9\pi^2}$ кг
Вычислим приближённое значение массы, приняв $\pi \approx 3.14$:
$m \approx \frac{40}{9 \cdot (3.14)^2} \approx \frac{40}{9 \cdot 9.8596} \approx \frac{40}{88.7364} \approx 0.4507$ кг
Округлим результат до двух значащих цифр.
Ответ: масса груза пружинного маятника составляет примерно 0,45 кг.
Другие задания:
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