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Консультация № 181257
12.12.2010, 22:34
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Здравствуйте, уважаемые эксперты! Прошу Вас ответить на следующий вопрос:
Точка участвует одновременно в двух взаимноперпендикулярных колебаниях x=asinωt и y=bsinωt. Найти траекторию движения.
Точка участвует одновременно в двух взаимноперпендикулярных колебаниях x=asinωt и y=bsinωt. Найти траекторию движения.
Обсуждение
13.12.2010, 06:33
общий
это ответ
Здравствуйте, Наталья Валерьевна!
Для того чтобы найти уравнение траектории движения необходимо исключить время. Из первого уравнения выразим sin[$969$]t=x/a и подставим данное значение во второе уравнение, в результате получим: y=b*x/a=b/a*x.
Т.е. получили уравнение y=b/a*x - представляющее собой прямую.
Угол наклона прямой равен: tg[$945$]=b/a, [$945$]=arctg(b/a)
Период результирующего колебания равен периоду слагаемых колебаний, а амплитуда равна: A=[$8730$](a2+b2)
Удачи
Для того чтобы найти уравнение траектории движения необходимо исключить время. Из первого уравнения выразим sin[$969$]t=x/a и подставим данное значение во второе уравнение, в результате получим: y=b*x/a=b/a*x.
Т.е. получили уравнение y=b/a*x - представляющее собой прямую.
Угол наклона прямой равен: tg[$945$]=b/a, [$945$]=arctg(b/a)
Период результирующего колебания равен периоду слагаемых колебаний, а амплитуда равна: A=[$8730$](a2+b2)
Удачи
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