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Консультация № 200091
14.01.2021, 03:27
0.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос: Материальная точка движется вдоль оси х так, что ее скорость зависит от координаты х по закону v=(a-bx^2)^1/2, где а=136 м^2/c^2, b=100 c^2.показать, что уравнение движения точки является динамическим уравнением гармонических колебаний и найти период т этих колебаний.
Обсуждение
16.01.2021, 00:34
общий
Адресаты:
Что-то у вас коэффициент b не согласуется - там, вероятно, показатель степени должен быть отрицательный? Проверьте, что написано в условии
Об авторе:
С уважением
shvetski
С уважением
shvetski
21.01.2021, 03:13
общий
это ответ
Здравствуйте, sport7@mail.ru!
Так как v = dx/dt, то зависимость скорости материальной точки от координаты можно записать как
откуда
и уравнение движения точки будет иметь вид
Это стандартное уравнение гармонических колебаний
с амплитудой x[sub]0[/sub] = [$8730$]a/b, круговой частотой [$969$] = [$8730$]b и некоторой начальной фазой [$966$]. В данном случае x[sub]0[/sub] = [$8730$]1.36 = 1.166 м и [$969$] = [$8730$]100 = 10 с[sup]-1[/sup]. Тогда период колебаний составит
Так как v = dx/dt, то зависимость скорости материальной точки от координаты можно записать как
откуда
и уравнение движения точки будет иметь вид
Это стандартное уравнение гармонических колебаний
с амплитудой x[sub]0[/sub] = [$8730$]a/b, круговой частотой [$969$] = [$8730$]b и некоторой начальной фазой [$966$]. В данном случае x[sub]0[/sub] = [$8730$]1.36 = 1.166 м и [$969$] = [$8730$]100 = 10 с[sup]-1[/sup]. Тогда период колебаний составит
5
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