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Задать вопрос экспертам

Консультация № 172630

25.09.2009, 18:56

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0 1 1

Образование

Здравствуйте, уважаемые эксперты! Пожалуйста, помогите решить задачу.

Точка совершает колебания по закону x=Asinwt. В некоторый момент времени смещения x1 точки оказался равным 5 см. Когда фаза колебаний увеличилась вдвое, смещение х2 стало равным 8 см. Найти амплитуду А колебаний.

Заранее спасибо.

Обсуждение

Неизвестный

26.09.2009, 01:51

общий

это ответ

Здравствуйте, Попов Антон Андреевич.
Составляем уравнения колебания для обоих случаев, получаем:
5=A*sinф ...........(1)
8=А*sin 2ф..........(2)
синус двойного аргумента sin2a=2*sina*cosa...(3)
тогда 8=2*A*sinф*cosф ......(4)
из 1 и 4 получаем
8=2*5*cosф ........(5)
отсюда cosф=0,8
вычисляем синус по основной формуле сумма квадратов синус и косинус =1, след. sinф=0,6
и тогда по формуле 1 вычисляем амплитуду A=5/sinф=5,0,6=8,3
вроде так, давно не решала
если не понятны обозначения или теория, то напишите в мини-форуме

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