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Консультация № 196657
12.10.2019, 11:43
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Точка участвует в двух взаимно-перпендикулярных колебаниях:
Х = 2 *sin (pi*t) см
Y = -2 * sin (pi*t) см.
Найти:
4) максимальное смещение точки от начала координат (в см);
5) скорость точки в начальный момент (в см/с);
6) угол между вектором скорости и осью Х в этот момент (в градусах).
Точка участвует в двух взаимно-перпендикулярных колебаниях:
Х = 2 *sin (pi*t) см
Y = -2 * sin (pi*t) см.
Найти:
4) максимальное смещение точки от начала координат (в см);
5) скорость точки в начальный момент (в см/с);
6) угол между вектором скорости и осью Х в этот момент (в градусах).
Обсуждение
13.10.2019, 08:58
общий
это ответ
Здравствуйте, arty324gh!
Решение
Из заданных уравнений движения точки следует, что
Чтобы получить уравнение траектории точки, исключим параметр 
из уравнений движения: 
Следовательно, траекторией движения точки является отрезок прямой линии 
концы которого -- точки 
Этот отрезок симметричен относительно начала координат. Поэтому максимальное смещение точки от начала координат составляет 
(см).
Дифференцируя уравнения движения точки, получим
см/с -- закон изменения проекции скорости точки на ось абсцисс; 
см/с -- закон изменения проекции скорости точки на ось ординат. Тогда 
см/с -- закон изменения модуля скорости точки. Поэтому в начальный момент времени скорость точки составляет 
(см/с).
В начальный момент времени
(см/с), 
(см/с). Поэтому 
(см/с) -- вектор скорости точки в начальный момент времени; из полученного выражения видно, что он составляет с осью абсцисс угол, равный 
Ответ: 4)
см; 5) 
см/с; 6)
Решение
Из заданных уравнений движения точки следует, что
Чтобы получить уравнение траектории точки, исключим параметр из уравнений движения: Следовательно, траекторией движения точки является отрезок прямой линии концы которого -- точки Этот отрезок симметричен относительно начала координат. Поэтому максимальное смещение точки от начала координат составляет (см).Дифференцируя уравнения движения точки, получим
см/с -- закон изменения проекции скорости точки на ось абсцисс; см/с -- закон изменения проекции скорости точки на ось ординат. Тогда см/с -- закон изменения модуля скорости точки. Поэтому в начальный момент времени скорость точки составляет (см/с).В начальный момент времени
(см/с), (см/с). Поэтому (см/с) -- вектор скорости точки в начальный момент времени; из полученного выражения видно, что он составляет с осью абсцисс угол, равный Ответ: 4)
см; 5) см/с; 6)
Об авторе:
Facta loquuntur.
Facta loquuntur.
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