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Вариант 4, страница 81 - гдз по физике 9 класс дидактические материалы Марон, Марон
Авторы: Марон А. Е., Марон Е. А.
Тип: Дидактические материалы
Издательство: Просвещение
Год издания: 2022 - 2026
Уровень обучения: базовый
Цвет обложки: белый изображена башня
ISBN: 978-5-09-111414-0
Популярные ГДЗ в 9 классе
Самостоятельные работы. СР-12. Механические колебания - страница 81.
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" => 1428673 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "81" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp12-4" "field_display_title" => "Вариант 4" "field_outside_task" => null "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 {#1073 #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" => 1428174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Самостоятельные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1038 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "53" "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 {#1037 #items: array:1 [ 0 => App\Models\Book {#1039 #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" => 894 "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 {#1040 #items: array:1 [ 0 => App\Models\Term {#1041 …30} ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ 0 => App\Models\Term {#1043 …30} ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1044 #items: array:1 [ 0 => App\Models\Term {#1045 …30} ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:2 [ 0 => App\Models\Term {#1047 …30} 1 => App\Models\Term {#1048 …30} ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1051 …30} ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 …30} ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 …30} ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058 #items: array:1 [ 0 => App\Models\Term {#1059 …30} ] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ 0 => App\Models\Term {#1061 …30} ] #escapeWhenCastingToString: false } "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 …30} ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "изображена башня" "field_publication_year" => "2022" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "674" "field_priority" => null "field_default_folder" => "/fizika_09/maron-dm/" "field_isbn" => "978-5-09-111414-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 …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" => 894 "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 {#1040} "field_class" => Illuminate\Database\Eloquent\Collection {#1042} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1044} "field_author" => Illuminate\Database\Eloquent\Collection {#1046} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_country" => Illuminate\Database\Eloquent\Collection {#1052} "field_city" => Illuminate\Database\Eloquent\Collection {#1054} "field_series" => Illuminate\Database\Eloquent\Collection {#1056} "field_umk" => Illuminate\Database\Eloquent\Collection {#1057} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060} "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064} "field_under_the_edition_degree" => null "field_cover_description" => "изображена башня" "field_publication_year" => "2022" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "674" "field_priority" => null "field_default_folder" => "/fizika_09/maron-dm/" "field_isbn" => "978-5-09-111414-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067} "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1428174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Самостоятельные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1038} "field_page_start" => "53" "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 {#1037} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1109 #items: array:2 [ 0 => App\Models\Branch {#1117 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1428174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Самостоятельные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1118 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "53" "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 {#1152 #items: array:1 [ 0 => App\Models\Book {#1119 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 894 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:1 [ 0 => App\Models\Term {#1120 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1122 #items: array:1 [ 0 => App\Models\Term {#1123 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1124 #items: array:1 [ 0 => App\Models\Term {#1125 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 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 {#1126 #items: array:2 [ 0 => App\Models\Term {#1127 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5107 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Марон" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Абрам" "field_patronymic" => "Евсеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 5107 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Марон" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Абрам" "field_patronymic" => "Евсеевич" "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 {#1128 #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" => 5108 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Марон" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "field_surname_rp" => null ] #original: array:12 [ "id" => 5108 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Марон" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "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 {#1129 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 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:10 [ "id" => 6510 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Дидактические материалы" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "дидактические материалы" "field_creative_case" => "дидактическими материалами" "field_dative_case" => "дидактическим материалам" "field_genitive_case" => "дидактических материалов" "field_nominative_case" => "дидактические материалы" "field_prepositional_case" => "дидактических материалах" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "didakticheskie materialy" ] #original: array:10 [ "id" => 6510 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Дидактические материалы" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "дидактические материалы" "field_creative_case" => "дидактическими материалами" "field_dative_case" => "дидактическим материалам" "field_genitive_case" => "дидактических материалов" "field_nominative_case" => "дидактические материалы" "field_prepositional_case" => "дидактических материалах" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "didakticheskie materialy" ] #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 {#1132 #items: array:1 [ 0 => 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: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 {#1134 #items: array:1 [ 0 => App\Models\Term {#1135 #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 {#1136 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1137 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => 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" => 38 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "базовый" "field_cases" => array:6 [ "field_accusative_case" => "базовый" "field_creative_case" => "базовым" "field_dative_case" => "базовому" "field_genitive_case" => "базового" "field_nominative_case" => "базовый" "field_prepositional_case" => "базовом" ] "field_translit" => "bazovyy" ] #original: array:6 [ "id" => 38 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "базовый" "field_cases" => array:6 [ "field_accusative_case" => "базовый" "field_creative_case" => "базовым" "field_dative_case" => "базовому" "field_genitive_case" => "базового" "field_nominative_case" => "базовый" "field_prepositional_case" => "базовом" ] "field_translit" => "bazovyy" ] #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_standart_of_education" => 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:10 [ "id" => 25 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (новый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => "красный" "field_end_year" => "2027" "field_start_year" => "2023" "field_translit" => "fgos" "field_type" => "новый" ] #original: array:10 [ "id" => 25 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (новый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => "красный" "field_end_year" => "2027" "field_start_year" => "2023" "field_translit" => "fgos" "field_type" => "новый" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1142 #items: array:1 [ 0 => App\Models\Term {#1143 #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" => 34 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное" "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" ] #original: array:6 [ "id" => 34 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное" "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" ] #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 {#1144 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "изображена башня" "field_publication_year" => "2022" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "674" "field_priority" => null "field_default_folder" => "/fizika_09/maron-dm/" "field_isbn" => "978-5-09-111414-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1147 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ 0 => App\Models\Term {#1149 #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" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ "field_accusative_case" => "белый" "field_creative_case" => "белым" "field_dative_case" => "белому" "field_genitive_case" => "белого" "field_nominative_case" => "белый" "field_prepositional_case" => "белом" ] "field_translit" => "belyy" ] #original: array:6 [ "id" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ "field_accusative_case" => "белый" "field_creative_case" => "белым" "field_dative_case" => "белому" "field_genitive_case" => "белого" "field_nominative_case" => "белый" "field_prepositional_case" => "белом" ] "field_translit" => "belyy" ] #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" => 894 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1121} "field_class" => Illuminate\Database\Eloquent\Collection {#1122} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1124} "field_author" => Illuminate\Database\Eloquent\Collection {#1126} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1129} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1130} "field_country" => Illuminate\Database\Eloquent\Collection {#1132} "field_city" => Illuminate\Database\Eloquent\Collection {#1134} "field_series" => Illuminate\Database\Eloquent\Collection {#1136} "field_umk" => Illuminate\Database\Eloquent\Collection {#1137} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1138} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1140} "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1142} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1144} "field_under_the_edition_degree" => null "field_cover_description" => "изображена башня" "field_publication_year" => "2022" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "674" "field_priority" => null "field_default_folder" => "/fizika_09/maron-dm/" "field_isbn" => "978-5-09-111414-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1145} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1146} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1147} "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1148} "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 {#1150 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1428174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Самостоятельные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1118} "field_page_start" => "53" "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 {#1152} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1150} ] #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 {#1151 #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" => 1428186 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "СР-12. Механические колебания" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1153 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "80" "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 {#1154 #items: array:1 [ 0 => App\Models\Book {#1119} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1155 #items: array:1 [ 0 => App\Models\Branch {#1035} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1428186 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "СР-12. Механические колебания" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1153} "field_page_start" => "80" "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 {#1154} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1155} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:2 [ 0 => App\Models\Element {#1100 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1682988 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Edition {#1098 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5992 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:1 [ 0 => App\Models\Term {#1099 …30} ] #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 {#1097 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1095 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5992 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096} "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 {#1097} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1095} "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" => "1428673" "type" => "task" ] "text" => "<p><strong>1.</strong> За 2 мин маятник совершил 120 колебаний. Когда длину маятника увеличили на 74,7 см, то он за то же время совершил 60 колебаний. Найдите начальную и конечную длины маятника и ускорение свободного падения в этом месте.</p><p><strong>2.</strong> Для чего все вибрирующие установки (моторы, генераторы и др.) ставятся на специальные амортизаторы?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1427" "height" => 429 "path" => "/media/fizika_09/maron-dm/0-cp12/4-1.webp?ts=1758964248" ] ] ] #original: array:7 [ "id" => 1682988 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090} "task" => array:2 [ "refs" => "1428673" "type" => "task" ] "text" => "<p><strong>1.</strong> За 2 мин маятник совершил 120 колебаний. Когда длину маятника увеличили на 74,7 см, то он за то же время совершил 60 колебаний. Найдите начальную и конечную длины маятника и ускорение свободного падения в этом месте.</p><p><strong>2.</strong> Для чего все вибрирующие установки (моторы, генераторы и др.) ставятся на специальные амортизаторы?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1427" "height" => 429 "path" => "/media/fizika_09/maron-dm/0-cp12/4-1.webp?ts=1758964248" ] ] ] #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 {#1093 #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" => 1730690 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1084 #items: array:1 [ 0 => App\Models\Edition {#1092 #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" => 6313 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1088 #items: array:1 [ 0 => App\Models\Term {#1091 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1089 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1087 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6313 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1088} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1089} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1086} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1087} "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" => "1428673" "type" => "task" ] "text" => "<p><strong>1.</strong> <strong>Дано:</strong></p><p>$t = 2$ мин<br>$N_1 = 120$<br>$\Delta l = 74,7$ см<br>$N_2 = 60$</p><p>$t = 2 \cdot 60 = 120$ c<br>$\Delta l = 74,7 / 100 = 0,747$ м</p><p><strong>Найти:</strong></p><p>$l_1$ - ?<br>$l_2$ - ?<br>$\text{g}$ - ?</p><p><strong>Решение:</strong></p><p>Период колебаний математического маятника определяется формулой: $T = 2\pi\sqrt{\frac{l}{g}}$, где $\text{l}$ - длина маятника, а $\text{g}$ - ускорение свободного падения.</p><p>Период также можно найти как отношение времени колебаний $\text{t}$ к числу полных колебаний $\text{N}$: $T = \frac{t}{N}$.</p><p>Найдем периоды колебаний маятника в первом и втором случаях:</p><p>$T_1 = \frac{t}{N_1} = \frac{120 \text{ c}}{120} = 1 \text{ c}$</p><p>$T_2 = \frac{t}{N_2} = \frac{120 \text{ c}}{60} = 2 \text{ c}$</p><p>Запишем формулы для периодов, обозначив начальную длину как $l_1$, а конечную как $l_2$:</p><p>$T_1 = 2\pi\sqrt{\frac{l_1}{g}}$</p><p>$T_2 = 2\pi\sqrt{\frac{l_2}{g}}$</p><p>Из условия известно, что конечная длина $l_2$ связана с начальной $l_1$ соотношением: $l_2 = l_1 + \Delta l$.</p><p>Чтобы найти связь между длинами, разделим уравнение для $T_2$ на уравнение для $T_1$:</p><p>$\frac{T_2}{T_1} = \frac{2\pi\sqrt{\frac{l_2}{g}}}{2\pi\sqrt{\frac{l_1}{g}}} = \sqrt{\frac{l_2}{l_1}}$</p><p>Подставим известные значения периодов:</p><p>$\frac{2 \text{ c}}{1 \text{ c}} = \sqrt{\frac{l_2}{l_1}}$</p><p>Возведем обе части уравнения в квадрат:</p><p>$4 = \frac{l_2}{l_1} \implies l_2 = 4l_1$</p><p>Теперь мы имеем систему из двух уравнений для длин:</p><p>$l_2 = 4l_1$<br>$l_2 = l_1 + \Delta l$</p><p>Приравняем правые части этих уравнений:</p><p>$4l_1 = l_1 + \Delta l$</p><p>$3l_1 = \Delta l$</p><p>Отсюда находим начальную длину маятника $l_1$:</p><p>$l_1 = \frac{\Delta l}{3} = \frac{0,747 \text{ м}}{3} = 0,249 \text{ м}$</p><p>Теперь найдем конечную длину $l_2$:</p><p>$l_2 = 4l_1 = 4 \cdot 0,249 \text{ м} = 0,996 \text{ м}$</p><p>Для нахождения ускорения свободного падения $\text{g}$ воспользуемся формулой для первого периода, выразив из нее $\text{g}$:</p><p>$T_1^2 = (2\pi\sqrt{\frac{l_1}{g}})^2 = 4\pi^2\frac{l_1}{g} \implies g = \frac{4\pi^2l_1}{T_1^2}$</p><p>Подставим численные значения:</p><p>$g = \frac{4\pi^2 \cdot 0,249 \text{ м}}{(1 \text{ с})^2} \approx 4 \cdot (3,1416)^2 \cdot 0,249 \approx 9,83 \text{ м/с}^2$</p><p><strong>Ответ:</strong> начальная длина маятника $l_1 = 0,249$ м (24,9 см), конечная длина $l_2 = 0,996$ м (99,6 см), ускорение свободного падения $g \approx 9,83 \text{ м/с}^2$.</p><p><strong>2.</strong> Все вибрирующие установки, такие как моторы и генераторы, устанавливаются на специальные амортизаторы для изоляции и гашения (демпфирования) механических колебаний. Основная цель — предотвратить передачу вибраций от работающего механизма на его основание (фундамент, пол, раму) и окружающую среду.</p><p>Это необходимо по нескольким ключевым причинам. Во-первых, для предотвращения разрушительного явления резонанса. Если частота вибраций установки совпадет с собственной частотой колебаний опорной конструкции, амплитуда колебаний резко возрастет, что может привести к быстрому разрушению и установки, и ее основания. Во-вторых, для снижения уровня шума, так как вибрации, передающиеся на большие поверхности (пол, стены), создают сильный низкочастотный гул. В-третьих, для защиты самой установки и несущих конструкций от преждевременного износа и усталостного разрушения материалов, вызываемого постоянными вибрационными нагрузками.</p><p>Амортизаторы, изготовленные из упругих и вязких материалов (например, резины или систем пружин с гасителями), поглощают энергию колебаний, превращая ее в тепло, и смещают собственную частоту системы в безопасную область, далеко от рабочей частоты установки. Таким образом, они обеспечивают безопасную и тихую эксплуатацию оборудования.</p><p><strong>Ответ:</strong> вибрирующие установки ставятся на специальные амортизаторы для того, чтобы изолировать их от опорных конструкций. Это позволяет предотвратить разрушение из-за резонанса, снизить уровень шума и защитить как саму установку, так и окружающие объекты от повреждений, вызываемых постоянной вибрацией.</p>" ] #original: array:6 [ "id" => 1730690 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1084} "task" => array:2 [ "refs" => "1428673" "type" => "task" ] "text" => "<p><strong>1.</strong> <strong>Дано:</strong></p><p>$t = 2$ мин<br>$N_1 = 120$<br>$\Delta l = 74,7$ см<br>$N_2 = 60$</p><p>$t = 2 \cdot 60 = 120$ c<br>$\Delta l = 74,7 / 100 = 0,747$ м</p><p><strong>Найти:</strong></p><p>$l_1$ - ?<br>$l_2$ - ?<br>$\text{g}$ - ?</p><p><strong>Решение:</strong></p><p>Период колебаний математического маятника определяется формулой: $T = 2\pi\sqrt{\frac{l}{g}}$, где $\text{l}$ - длина маятника, а $\text{g}$ - ускорение свободного падения.</p><p>Период также можно найти как отношение времени колебаний $\text{t}$ к числу полных колебаний $\text{N}$: $T = \frac{t}{N}$.</p><p>Найдем периоды колебаний маятника в первом и втором случаях:</p><p>$T_1 = \frac{t}{N_1} = \frac{120 \text{ c}}{120} = 1 \text{ c}$</p><p>$T_2 = \frac{t}{N_2} = \frac{120 \text{ c}}{60} = 2 \text{ c}$</p><p>Запишем формулы для периодов, обозначив начальную длину как $l_1$, а конечную как $l_2$:</p><p>$T_1 = 2\pi\sqrt{\frac{l_1}{g}}$</p><p>$T_2 = 2\pi\sqrt{\frac{l_2}{g}}$</p><p>Из условия известно, что конечная длина $l_2$ связана с начальной $l_1$ соотношением: $l_2 = l_1 + \Delta l$.</p><p>Чтобы найти связь между длинами, разделим уравнение для $T_2$ на уравнение для $T_1$:</p><p>$\frac{T_2}{T_1} = \frac{2\pi\sqrt{\frac{l_2}{g}}}{2\pi\sqrt{\frac{l_1}{g}}} = \sqrt{\frac{l_2}{l_1}}$</p><p>Подставим известные значения периодов:</p><p>$\frac{2 \text{ c}}{1 \text{ c}} = \sqrt{\frac{l_2}{l_1}}$</p><p>Возведем обе части уравнения в квадрат:</p><p>$4 = \frac{l_2}{l_1} \implies l_2 = 4l_1$</p><p>Теперь мы имеем систему из двух уравнений для длин:</p><p>$l_2 = 4l_1$<br>$l_2 = l_1 + \Delta l$</p><p>Приравняем правые части этих уравнений:</p><p>$4l_1 = l_1 + \Delta l$</p><p>$3l_1 = \Delta l$</p><p>Отсюда находим начальную длину маятника $l_1$:</p><p>$l_1 = \frac{\Delta l}{3} = \frac{0,747 \text{ м}}{3} = 0,249 \text{ м}$</p><p>Теперь найдем конечную длину $l_2$:</p><p>$l_2 = 4l_1 = 4 \cdot 0,249 \text{ м} = 0,996 \text{ м}$</p><p>Для нахождения ускорения свободного падения $\text{g}$ воспользуемся формулой для первого периода, выразив из нее $\text{g}$:</p><p>$T_1^2 = (2\pi\sqrt{\frac{l_1}{g}})^2 = 4\pi^2\frac{l_1}{g} \implies g = \frac{4\pi^2l_1}{T_1^2}$</p><p>Подставим численные значения:</p><p>$g = \frac{4\pi^2 \cdot 0,249 \text{ м}}{(1 \text{ с})^2} \approx 4 \cdot (3,1416)^2 \cdot 0,249 \approx 9,83 \text{ м/с}^2$</p><p><strong>Ответ:</strong> начальная длина маятника $l_1 = 0,249$ м (24,9 см), конечная длина $l_2 = 0,996$ м (99,6 см), ускорение свободного падения $g \approx 9,83 \text{ м/с}^2$.</p><p><strong>2.</strong> Все вибрирующие установки, такие как моторы и генераторы, устанавливаются на специальные амортизаторы для изоляции и гашения (демпфирования) механических колебаний. Основная цель — предотвратить передачу вибраций от работающего механизма на его основание (фундамент, пол, раму) и окружающую среду.</p><p>Это необходимо по нескольким ключевым причинам. Во-первых, для предотвращения разрушительного явления резонанса. Если частота вибраций установки совпадет с собственной частотой колебаний опорной конструкции, амплитуда колебаний резко возрастет, что может привести к быстрому разрушению и установки, и ее основания. Во-вторых, для снижения уровня шума, так как вибрации, передающиеся на большие поверхности (пол, стены), создают сильный низкочастотный гул. В-третьих, для защиты самой установки и несущих конструкций от преждевременного износа и усталостного разрушения материалов, вызываемого постоянными вибрационными нагрузками.</p><p>Амортизаторы, изготовленные из упругих и вязких материалов (например, резины или систем пружин с гасителями), поглощают энергию колебаний, превращая ее в тепло, и смещают собственную частоту системы в безопасную область, далеко от рабочей частоты установки. Таким образом, они обеспечивают безопасную и тихую эксплуатацию оборудования.</p><p><strong>Ответ:</strong> вибрирующие установки ставятся на специальные амортизаторы для того, чтобы изолировать их от опорных конструкций. Это позволяет предотвратить разрушение из-за резонанса, снизить уровень шума и защитить как саму установку, так и окружающие объекты от повреждений, вызываемых постоянной вибрацией.</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" => "1428674" "type" => "task" ] "previous" => array:2 [ "refs" => "1428672" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Book {#1119} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ 0 => App\Models\BookPage {#1076 #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" => 1428972 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "81" "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/page-81" "field_display_title" => "81" "field_folder" => "1" "field_image_name" => "81" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:1 [ 0 => App\Models\Book {#1119} ] #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 {#1107 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1160 #items: array:1 [ 0 => App\Models\Element {#1159 #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" => 1683639 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1161 #items: array:1 [ 0 => App\Models\Edition {#1098} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1428972" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "81-1.jpg" "alt" => null "width" => "1577" "height" => 2519 "path" => "/media/fizika_09/maron-dm/0-1/81-1.webp?ts=1758964766" ] ] ] #original: array:6 [ "id" => 1683639 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1161} "book_page" => array:2 [ "refs" => "1428972" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "81-1.jpg" "alt" => null "width" => "1577" "height" => 2519 "path" => "/media/fizika_09/maron-dm/0-1/81-1.webp?ts=1758964766" ] ] ] #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" => "1428973" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1428971" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1254 #items: array:6 [ 0 => App\Models\Task {#1266 #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" => 1428672 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "80" "field_page_end" => "81" "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp12-3" "field_display_title" => "Вариант 3" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1267 #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 {#1268 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1269 #items: array:1 [ 0 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1270 #items: array:2 [ 0 => App\Models\Branch {#1117} 1 => App\Models\Branch {#1151} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1272 #items: array:2 [ 0 => App\Models\Element {#1281 …30} 1 => App\Models\Element {#1283 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1428673" "type" => "task" ] "previous" => array:2 [ "refs" => "1428671" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1278 #items: array:1 [ 0 => App\Models\Book {#1119} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1428971" "type" => "book_page" ] ] #original: array:24 [ "id" => 1428672 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "80" "field_page_end" => "81" "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp12-3" "field_display_title" => "Вариант 3" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1267} "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 {#1268} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1269} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1270} "content" => Illuminate\Database\Eloquent\Collection {#1272} "next" => array:2 [ "refs" => "1428673" "type" => "task" ] "previous" => array:2 [ "refs" => "1428671" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1278} "page" => array:2 [ "refs" => "1428971" "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 {#1273 #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" => 1428673 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "81" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp12-4" "field_display_title" => "Вариант 4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1271 #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 {#1280 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1276 #items: array:1 [ 0 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1274 #items: array:2 [ 0 => App\Models\Branch {#1117} 1 => App\Models\Branch {#1151} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1277 #items: array:2 [ 0 => App\Models\Element {#1100} 1 => App\Models\Element {#1093} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1428674" "type" => "task" ] "previous" => array:2 [ "refs" => "1428672" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1275 #items: array:1 [ 0 => App\Models\Book {#1119} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1428972" "type" => "book_page" ] ] #original: array:24 [ "id" => 1428673 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "81" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp12-4" "field_display_title" => "Вариант 4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1271} "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 {#1280} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1276} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1274} "content" => Illuminate\Database\Eloquent\Collection {#1277} "next" => array:2 [ "refs" => "1428674" "type" => "task" ] "previous" => array:2 [ "refs" => "1428672" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1275} "page" => array:2 [ "refs" => "1428972" "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 {#1285 #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" => 1428674 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "81" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp12-5" "field_display_title" => "Вариант 5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1286 #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 {#1287 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1288 #items: array:1 [ 0 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1289 #items: array:2 [ 0 => App\Models\Branch {#1117} 1 => App\Models\Branch {#1151} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1291 #items: array:2 [ 0 => App\Models\Element {#1300 …30} 1 => App\Models\Element {#1302 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1428675" "type" => "task" ] "previous" => array:2 [ "refs" => "1428673" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1297 #items: array:1 [ 0 => App\Models\Book {#1119} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1428972" "type" => "book_page" ] ] #original: array:24 [ "id" => 1428674 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "81" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp12-5" "field_display_title" => "Вариант 5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1286} "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 {#1287} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1288} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1289} "content" => Illuminate\Database\Eloquent\Collection {#1291} "next" => array:2 [ "refs" => "1428675" "type" => "task" ] "previous" => array:2 [ "refs" => "1428673" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1297} "page" => array:2 [ "refs" => "1428972" "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 {#1292 #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" => 1428675 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "81" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp12-6" "field_display_title" => "Вариант 6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1290 #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 {#1299 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1295 #items: array:1 [ 0 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1293 #items: array:2 [ 0 => App\Models\Branch {#1117} 1 => App\Models\Branch {#1151} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1294 #items: array:2 [ 0 => App\Models\Element {#1312 …30} 1 => App\Models\Element {#1314 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1428676" "type" => "task" ] "previous" => array:2 [ "refs" => "1428674" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1309 #items: array:1 [ 0 => App\Models\Book {#1119} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1428972" "type" => "book_page" ] ] #original: array:24 [ "id" => 1428675 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "81" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp12-6" "field_display_title" => "Вариант 6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1290} "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 {#1299} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1295} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1293} "content" => Illuminate\Database\Eloquent\Collection {#1294} "next" => array:2 [ "refs" => "1428676" "type" => "task" ] "previous" => array:2 [ "refs" => "1428674" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1309} "page" => array:2 [ "refs" => "1428972" "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 {#1304 #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" => 1428676 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "81" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp13-1" "field_display_title" => "Вариант 1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1296 #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 {#1311 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1307 #items: array:1 [ 0 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1350 #items: array:2 [ 0 => App\Models\Branch {#1358 …30} 1 => App\Models\Branch {#1362 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1305 #items: array:2 [ 0 => App\Models\Element {#1341 …30} 1 => App\Models\Element {#1340 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1428677" "type" => "task" ] "previous" => array:2 [ "refs" => "1428675" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1344 #items: array:1 [ 0 => App\Models\Book {#1119} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1428972" "type" => "book_page" ] ] #original: array:24 [ "id" => 1428676 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "81" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp13-1" "field_display_title" => "Вариант 1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1296} "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 {#1311} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1307} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1350} "content" => Illuminate\Database\Eloquent\Collection {#1305} "next" => array:2 [ "refs" => "1428677" "type" => "task" ] "previous" => array:2 [ "refs" => "1428675" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1344} "page" => array:2 [ "refs" => "1428972" "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 => "*" ] } 5 => App\Models\Task {#1347 #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" => 1428677 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "81" "field_page_end" => "82" "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp13-2" "field_display_title" => "Вариант 2" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1355 #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 {#1342 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1345 #items: array:1 [ 0 => App\Models\Branch {#1358 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1308 #items: array:2 [ 0 => App\Models\Branch {#1358 …30} 1 => App\Models\Branch {#1362 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1316 #items: array:2 [ 0 => App\Models\Element {#1330 …30} …1 ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1428678" "type" => "task" ] "previous" => array:2 [ "refs" => "1428676" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1331 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1428972" "type" => "book_page" ] ] #original: array:24 [ "id" => 1428677 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "81" "field_page_end" => "82" "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp13-2" "field_display_title" => "Вариант 2" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1355} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => 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Вариант 4 (с. 81)
Условие. Вариант 4 (с. 81)
скриншот условия
1. За 2 мин маятник совершил 120 колебаний. Когда длину маятника увеличили на 74,7 см, то он за то же время совершил 60 колебаний. Найдите начальную и конечную длины маятника и ускорение свободного падения в этом месте.
2. Для чего все вибрирующие установки (моторы, генераторы и др.) ставятся на специальные амортизаторы?
Решение. Вариант 4 (с. 81)
1. Дано:
$t = 2$ мин
$N_1 = 120$
$\Delta l = 74,7$ см
$N_2 = 60$
$t = 2 \cdot 60 = 120$ c
$\Delta l = 74,7 / 100 = 0,747$ м
Найти:
$l_1$ - ?
$l_2$ - ?
$\text{g}$ - ?
Решение:
Период колебаний математического маятника определяется формулой: $T = 2\pi\sqrt{\frac{l}{g}}$, где $\text{l}$ - длина маятника, а $\text{g}$ - ускорение свободного падения.
Период также можно найти как отношение времени колебаний $\text{t}$ к числу полных колебаний $\text{N}$: $T = \frac{t}{N}$.
Найдем периоды колебаний маятника в первом и втором случаях:
$T_1 = \frac{t}{N_1} = \frac{120 \text{ c}}{120} = 1 \text{ c}$
$T_2 = \frac{t}{N_2} = \frac{120 \text{ c}}{60} = 2 \text{ c}$
Запишем формулы для периодов, обозначив начальную длину как $l_1$, а конечную как $l_2$:
$T_1 = 2\pi\sqrt{\frac{l_1}{g}}$
$T_2 = 2\pi\sqrt{\frac{l_2}{g}}$
Из условия известно, что конечная длина $l_2$ связана с начальной $l_1$ соотношением: $l_2 = l_1 + \Delta l$.
Чтобы найти связь между длинами, разделим уравнение для $T_2$ на уравнение для $T_1$:
$\frac{T_2}{T_1} = \frac{2\pi\sqrt{\frac{l_2}{g}}}{2\pi\sqrt{\frac{l_1}{g}}} = \sqrt{\frac{l_2}{l_1}}$
Подставим известные значения периодов:
$\frac{2 \text{ c}}{1 \text{ c}} = \sqrt{\frac{l_2}{l_1}}$
Возведем обе части уравнения в квадрат:
$4 = \frac{l_2}{l_1} \implies l_2 = 4l_1$
Теперь мы имеем систему из двух уравнений для длин:
$l_2 = 4l_1$
$l_2 = l_1 + \Delta l$
Приравняем правые части этих уравнений:
$4l_1 = l_1 + \Delta l$
$3l_1 = \Delta l$
Отсюда находим начальную длину маятника $l_1$:
$l_1 = \frac{\Delta l}{3} = \frac{0,747 \text{ м}}{3} = 0,249 \text{ м}$
Теперь найдем конечную длину $l_2$:
$l_2 = 4l_1 = 4 \cdot 0,249 \text{ м} = 0,996 \text{ м}$
Для нахождения ускорения свободного падения $\text{g}$ воспользуемся формулой для первого периода, выразив из нее $\text{g}$:
$T_1^2 = (2\pi\sqrt{\frac{l_1}{g}})^2 = 4\pi^2\frac{l_1}{g} \implies g = \frac{4\pi^2l_1}{T_1^2}$
Подставим численные значения:
$g = \frac{4\pi^2 \cdot 0,249 \text{ м}}{(1 \text{ с})^2} \approx 4 \cdot (3,1416)^2 \cdot 0,249 \approx 9,83 \text{ м/с}^2$
Ответ: начальная длина маятника $l_1 = 0,249$ м (24,9 см), конечная длина $l_2 = 0,996$ м (99,6 см), ускорение свободного падения $g \approx 9,83 \text{ м/с}^2$.
2. Все вибрирующие установки, такие как моторы и генераторы, устанавливаются на специальные амортизаторы для изоляции и гашения (демпфирования) механических колебаний. Основная цель — предотвратить передачу вибраций от работающего механизма на его основание (фундамент, пол, раму) и окружающую среду.
Это необходимо по нескольким ключевым причинам. Во-первых, для предотвращения разрушительного явления резонанса. Если частота вибраций установки совпадет с собственной частотой колебаний опорной конструкции, амплитуда колебаний резко возрастет, что может привести к быстрому разрушению и установки, и ее основания. Во-вторых, для снижения уровня шума, так как вибрации, передающиеся на большие поверхности (пол, стены), создают сильный низкочастотный гул. В-третьих, для защиты самой установки и несущих конструкций от преждевременного износа и усталостного разрушения материалов, вызываемого постоянными вибрационными нагрузками.
Амортизаторы, изготовленные из упругих и вязких материалов (например, резины или систем пружин с гасителями), поглощают энергию колебаний, превращая ее в тепло, и смещают собственную частоту системы в безопасную область, далеко от рабочей частоты установки. Таким образом, они обеспечивают безопасную и тихую эксплуатацию оборудования.
Ответ: вибрирующие установки ставятся на специальные амортизаторы для того, чтобы изолировать их от опорных конструкций. Это позволяет предотвратить разрушение из-за резонанса, снизить уровень шума и защитить как саму установку, так и окружающие объекты от повреждений, вызываемых постоянной вибрацией.
Другие задания:
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