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Консультация № 108528
08.11.2007, 07:45
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Уважаемые эксперты, пожалуйста помогите решить задачки. Заранее большое спасибо. C уважение Роман Александрович.
1) Уравнение незатухающих колебаний дано в виде x = sin 2,5 ∏t см. Найти смещение от положения равновесия, скорость и ускорение точки, находящейся на расстоянии 20 м. от источника колебаний, для момента t = 1с. после начала колебаний. Скорость распространения колебаний 100 м/c.
1) Уравнение незатухающих колебаний дано в виде x = sin 2,5 ∏t см. Найти смещение от положения равновесия, скорость и ускорение точки, находящейся на расстоянии 20 м. от источника колебаний, для момента t = 1с. после начала колебаний. Скорость распространения колебаний 100 м/c.
Обсуждение
Неизвестный
09.11.2007, 08:24
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это ответ
Здравствуйте, Чурнов Роман Александрович!
Уравнение незатухающих колебаний дано в виде x = sin 2,5 ∏t см. Найти смещение от положения равновесия, скорость и ускорение точки,
находящейся на расстоянии 20 м. от источника колебаний, для момента t = 1с. после начала колебаний.
Скорость распространения колебаний 100 м/c.
Уравнение колебаний точки на расстоянии y от источника колебаний запишется как x = sin[2,5 ∏(t - y/c)].
Скорость этой точки - производная смещения по времени: v = 2,5∏*cos[2,5 ∏(t - y/c)].
Ускорение точки - производная скорости по времени: a = -(2,5∏)^2*sin[2,5 ∏(t - y/c)].
При подстановке наших величин получим, что 2,5 ∏(t - y/c) = 2,5 ∏(1 - 20/100) = 2∏.
Тогда x = 0, v = 2,5∏, a = 0
Уравнение незатухающих колебаний дано в виде x = sin 2,5 ∏t см. Найти смещение от положения равновесия, скорость и ускорение точки,
находящейся на расстоянии 20 м. от источника колебаний, для момента t = 1с. после начала колебаний.
Скорость распространения колебаний 100 м/c.
Уравнение колебаний точки на расстоянии y от источника колебаний запишется как x = sin[2,5 ∏(t - y/c)].
Скорость этой точки - производная смещения по времени: v = 2,5∏*cos[2,5 ∏(t - y/c)].
Ускорение точки - производная скорости по времени: a = -(2,5∏)^2*sin[2,5 ∏(t - y/c)].
При подстановке наших величин получим, что 2,5 ∏(t - y/c) = 2,5 ∏(1 - 20/100) = 2∏.
Тогда x = 0, v = 2,5∏, a = 0
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