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Задать вопрос экспертам

Консультация № 189255

24.04.2016, 13:37

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Образование

Здравствуйте, уважаемые эксперты! Прошу помощи в следующем вопросе:
Шар радиуса R = 0,154 м закреплён на горизонтальной оси, проходящей через середину радиуса.
Коэффициент затухания равен b(бэта) = 2,48 с^(-1).
Найти резонансную частоту и начальную фазу (фи)0 вынужденных колебаний.

Обсуждение

давно

Roman Chaplinsky / Химик CH

Модератор
156417
2175

24.04.2016, 18:20

общий

это ответ

Здравствуйте, toph_bf!
момент инерции I=2mR²/5+m(R/2)²=0,65mR²
момент силы тяжести при отклонении от положения равновесия на угол [$945$]
-M=(R/2)mg[$183$]sin[$945$]
частота незатухающих малых колебаний
[$969$]₀²=-M/I[$945$]=g/1,3R
[$969$]₀=[$8730$](g/1,3R)=7,00 рад/с
резонансная частота вынужденных колебаний
[$969$]_рез=[$8730$]([$969$]₀²-2[$946$]²)=6,05 рад/с
начальная фаза резонансного колебаний
tg[$966$]=([$969$]₀²-[$969$]²)/2[$946$][$969$]
tg[$966$]_рез=([$969$]₀²-[$969$]_рез²)/2[$946$][$969$]_рез=2[$946$]²/2[$946$][$969$]_рез=[$946$]/[$969$]_рез=0,41
[$966$]_рез=0,39 рад=22,3[$176$]

С теоретическими материалами по вынужденным колебаниям можете ознакомиться, например, здесь и здесь.

5

Большое спасибо!

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