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Консультация № 196461
27.09.2019, 06:04
0.00 руб.
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1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Груз подвешен на пружине и имеет статическое отклонение δст = 0,08 м. Верхний конец пружины совершает вертикальные простые гармонические колебания с амплитудой А = 0,025 м и угловой частотой ω = 180 с-1. Найти амплитуду вынужденных вертикальных колебаний груза.
Груз подвешен на пружине и имеет статическое отклонение δст = 0,08 м. Верхний конец пружины совершает вертикальные простые гармонические колебания с амплитудой А = 0,025 м и угловой частотой ω = 180 с-1. Найти амплитуду вынужденных вертикальных колебаний груза.
Обсуждение
28.09.2019, 13:52
общий
это ответ
Здравствуйте, dar777!
Пусть
W -- вес груза;
k -- жёсткость пружины;
[$948$]ст=W/k [1, с. 16];
g -- ускорение свободного падения;
A=a -- амплитуда колебаний верхнего конца пружины;
p2=kg/W -- квадрат частоты колебаний груза [1, с. 56].
В соответствии с формулой (1.28) [1, с. 57], установившиеся вынужденные колебания груза относительно смещающегося верхнего конца пружины описываются уравнением
Значит, амплитуда этих колебаний составляет
Литература
1. Тимошенко С. П., Янг Д. Х., Уивер У. Колебания в инженерном деле. -- М.: Машиностроение, 1985. -- 472 с.
Полученный результат представляется "весьма малым", однако ошибки в расчёте я не нашёл.
Пусть
W -- вес груза;
k -- жёсткость пружины;
[$948$]ст=W/k [1, с. 16];
g -- ускорение свободного падения;
A=a -- амплитуда колебаний верхнего конца пружины;
p2=kg/W -- квадрат частоты колебаний груза [1, с. 56].
В соответствии с формулой (1.28) [1, с. 57], установившиеся вынужденные колебания груза относительно смещающегося верхнего конца пружины описываются уравнением
x*=(-Wa/(kg)sin[$969$]t)(1/(1-[$969$]2/p2)).
Значит, амплитуда этих колебаний составляет
A*=-Wa/(kg)(1/(1-[$969$]2/p2))=-Wa/(kg)(1/(1-[$969$]2W/(kg)))=-[$948$]стa/g(1/(1-[$969$]2[$948$]ст/g))=
=-0,08*0,025/9,81*1/(1-1802*0,08/9,81)[$8776$]7,75*10-7 (м).
Литература
1. Тимошенко С. П., Янг Д. Х., Уивер У. Колебания в инженерном деле. -- М.: Машиностроение, 1985. -- 472 с.
Полученный результат представляется "весьма малым", однако ошибки в расчёте я не нашёл.
5
Это самое лучшее решение!
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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