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Консультация № 202639
17.04.2022, 21:01
0.00 руб.
1
1
0
Здравствуйте, уважаемые эксперты! Прошу помочь в решении данной задачи:
Двойная пружина, состоит из двух последовательно включенных пружин с разными коэффициентами жесткости
и 
. Найти уравнение движения груза массы 
подвешенного на указанной двойной пружине, если в начальный момент он находился ниже положения равновесия на расстоянии 
, и ему сообщили скорость 
, направленную вверх.
Ответ:
Спасибо!
Двойная пружина, состоит из двух последовательно включенных пружин с разными коэффициентами жесткости
и . Найти уравнение движения груза массы подвешенного на указанной двойной пружине, если в начальный момент он находился ниже положения равновесия на расстоянии , и ему сообщили скорость , направленную вверх.Ответ:
Спасибо!
Прикрепленные файлы:
Обсуждение
18.04.2022, 15:59
общий
Адресаты:
Вы просили "Прошу помочь в решении", но не сообщили, в какой именно помощи Вы нуждаетесь?
Если Вы не знаете уравнения пружинного маятника, то почитайте соответствующую учебную статью, например "Свободные колебания пружинного маятника. Общие сведения" pandia.ru/text/77/494/49063.php (Ссылка)
Если Вас пугает необычное усложнение 2 пружины вместо одной, то, учитывая последовательное соединение пружин, составьте систему простых уравнений Гука:
F = c1·x1[$8195$] ;[$8195$] F = c2·x2[$8195$] [$8658$]
F / c1 = x1[$8195$] ;[$8195$] F / c2 = x2
Нас интересует суммарное удлинение "x" от 2х пружин, а не частные удлинения x1 и x2 , поэтому суммируем уравнения почленно:
F / c1 + F / c2 = x1 + x2 = x
Тогда F = x / (1 / c1 + 1 / c2) = c1·c2·x / (c1 + c2) = k·x , где эквивалентный коэффициент жесткости двойной пружины равен
k = c1·c2 / (c1 + c2)
И Ваш Ответ существенно упростится: x = x0·cos[[$8730$](k/m)]·t - V0·[$8730$](m/k)·sin[[$8730$](k/m)]·t
Дальше сами справитесь?
Если Вы не знаете уравнения пружинного маятника, то почитайте соответствующую учебную статью, например "Свободные колебания пружинного маятника. Общие сведения" pandia.ru/text/77/494/49063.php (Ссылка)
Если Вас пугает необычное усложнение 2 пружины вместо одной, то, учитывая последовательное соединение пружин, составьте систему простых уравнений Гука:
F = c1·x1[$8195$] ;[$8195$] F = c2·x2[$8195$] [$8658$]
F / c1 = x1[$8195$] ;[$8195$] F / c2 = x2
Нас интересует суммарное удлинение "x" от 2х пружин, а не частные удлинения x1 и x2 , поэтому суммируем уравнения почленно:
F / c1 + F / c2 = x1 + x2 = x
Тогда F = x / (1 / c1 + 1 / c2) = c1·c2·x / (c1 + c2) = k·x , где эквивалентный коэффициент жесткости двойной пружины равен
k = c1·c2 / (c1 + c2)
И Ваш Ответ существенно упростится: x = x0·cos[[$8730$](k/m)]·t - V0·[$8730$](m/k)·sin[[$8730$](k/m)]·t
Дальше сами справитесь?
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