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Консультация № 175628
26.12.2009, 20:25
45.00 руб.
0
5
1
Здравствуйте, уважаемые эксперты, необходима Ваша помощь в решении контрольной работы(часть 1):
1. Колебания материальной точки происходят согласно уравнению x=A*cosωt, где A=8см, ω=2π/6с^-1. В момент, когда возращающая сила в первый раз достигла значения -5мН, потенциальная энергия точки стала равной 100мкДж. Найти этот момент времени и соответствующую ему фазу ωt.
2. Точка участвует одновременно в двух гармонических колебаниях, происходящих во взаимно перпендикулярных направлениях и описывается уравнениями х=3cos(ωt) см и у= 4cos(ωt) cм. Определить уравнение точки и вычертить её с нанесением масштаба.
3. Колебательный контур состоит из катушки индуктивностью 20мкГн и конденсатора емкостью 80нФ. Величина емкости может отклоняться от заданного значения на 2%. Вычислить, в каких пределах может изменяться длина волны, на которую резонирует контур.
1. Колебания материальной точки происходят согласно уравнению x=A*cosωt, где A=8см, ω=2π/6с^-1. В момент, когда возращающая сила в первый раз достигла значения -5мН, потенциальная энергия точки стала равной 100мкДж. Найти этот момент времени и соответствующую ему фазу ωt.
2. Точка участвует одновременно в двух гармонических колебаниях, происходящих во взаимно перпендикулярных направлениях и описывается уравнениями х=3cos(ωt) см и у= 4cos(ωt) cм. Определить уравнение точки и вычертить её с нанесением масштаба.
3. Колебательный контур состоит из катушки индуктивностью 20мкГн и конденсатора емкостью 80нФ. Величина емкости может отклоняться от заданного значения на 2%. Вычислить, в каких пределах может изменяться длина волны, на которую резонирует контур.
Обсуждение
Неизвестный
26.12.2009, 20:29
общий
Поправка Задача 2. Описка - у= 4cos(ωt) cм, правильно будет - у= 4cos(ωt+π) cм
Неизвестный
26.12.2009, 21:36
общий
27.12.2009, 08:50
это ответ
Здравствуйте, Robshnider.
1. F=-kx cила
E=k(x^2)/2 потенциальная энергия,
откуда находим что x=-2E/F=0.1/5=0.02 м=2 см.
В рассматриваемый момент сos (wt)=x/A=0.25. Откуда wt=п/2.38. t=1.26 c.
2. y= 4cos(ωt+π)=- 4cos(ωt)=-4x/3. Это отрезок прямой y=-4x/3 -3<=x<=3. Думаю такую прямую вы начертить сможете.
3. [$955$]=2п/w=2п(LC)^0.5
[$916$][$955$]=2п((LC)^0.5)((1+ [$916$]C/C)^1/2-1)=п((LC)^0.5)*( [$916$]C/C)=3.14*1.265*10^(-6)*0.02=7.94 * 10^(-8) м=79.4 нм.
1. F=-kx cила
E=k(x^2)/2 потенциальная энергия,
откуда находим что x=-2E/F=0.1/5=0.02 м=2 см.
В рассматриваемый момент сos (wt)=x/A=0.25. Откуда wt=п/2.38. t=1.26 c.
2. y= 4cos(ωt+π)=- 4cos(ωt)=-4x/3. Это отрезок прямой y=-4x/3 -3<=x<=3. Думаю такую прямую вы начертить сможете.
3. [$955$]=2п/w=2п(LC)^0.5
[$916$][$955$]=2п((LC)^0.5)((1+ [$916$]C/C)^1/2-1)=п((LC)^0.5)*( [$916$]C/C)=3.14*1.265*10^(-6)*0.02=7.94 * 10^(-8) м=79.4 нм.
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