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Консультация № 186097
19.05.2012, 11:04
92.47 руб.
0
2
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Колебательный контур состоит из конденсатора ёмкостью с=7мкф, катушки с индуктивностью ℒ=0,232 Гн и сопротивления R=40 Ом. Обкладкам конденсатора сообщен заряд gm=0,56 мКл. Найти период Т колебаний контура и логарифмический декремент затухания колебаний λ . Написать уравнение изменения со временем разности потенциалов u(t) на обкладках конденсатора. Найти разность потенциалов в момент времени t=T|2.
Колебательный контур состоит из конденсатора ёмкостью с=7мкф, катушки с индуктивностью ℒ=0,232 Гн и сопротивления R=40 Ом. Обкладкам конденсатора сообщен заряд gm=0,56 мКл. Найти период Т колебаний контура и логарифмический декремент затухания колебаний λ . Написать уравнение изменения со временем разности потенциалов u(t) на обкладках конденсатора. Найти разность потенциалов в момент времени t=T|2.
Обсуждение
19.05.2012, 21:41
общий
21.05.2012, 00:58
это ответ
Здравствуйте, Посетитель - 373608!
Закон Ома для рассматриваемого колебательного контура записывается в виде
где
- напряжение на конденсаторе, 
- заряд конденсатора, 
- ток в цепи.
Если в качестве переменной величины выбрать заряд конденсатора, то уравнение свободных колебаний в контуре можно привести к такому виду:
или
Решением дифференциального уравнения (2) является
где
- коэффициент затухания колебаний,
- угловая частота колебаний в контуре. В нашем случае можно положить
Условный период затухающих колебаний
а логарифмический декремент затухания
Между напряжением на конденсаторе и зарядом существует соотношение
С учётом параметров рассматриваемого контура получаем по формулам (4), (5), (6):
период колебаний в контуре
логарифмический декремент затухания колебаний
В соответствии с этими результатами и формулами (3), (8) находим:
уравнение изменения со временем разности потенциалов на обкладках конденсатора
разность потенциалов в момент времени
С уважением.
Закон Ома для рассматриваемого колебательного контура записывается в виде
где
- напряжение на конденсаторе, - заряд конденсатора, - ток в цепи.Если в качестве переменной величины выбрать заряд конденсатора, то уравнение свободных колебаний в контуре можно привести к такому виду:
или
Решением дифференциального уравнения (2) является
где
- коэффициент затухания колебаний,
- угловая частота колебаний в контуре. В нашем случае можно положить
Условный период затухающих колебаний
а логарифмический декремент затухания
Между напряжением на конденсаторе и зарядом существует соотношение
С учётом параметров рассматриваемого контура получаем по формулам (4), (5), (6):
период колебаний в контуре
логарифмический декремент затухания колебаний
В соответствии с этими результатами и формулами (3), (8) находим:
уравнение изменения со временем разности потенциалов на обкладках конденсатора
разность потенциалов в момент времени
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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