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Консультация № 173879
01.11.2009, 13:14
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Здравствуйте уважаемые эксперты! помогите пожалуйста вывести формулу для решения задачи:
Определить, насколько резонансная частота отличается от частоты ν0 =1кГц собственный
колебаний системы, характеризуемой коэффициентом затухания β = 400 с-1.
ЗАРАНЕЕ БОЛЬШОЕ СПАСИБО!!!!!!!!!!!!
Определить, насколько резонансная частота отличается от частоты ν0 =1кГц собственный
колебаний системы, характеризуемой коэффициентом затухания β = 400 с-1.
ЗАРАНЕЕ БОЛЬШОЕ СПАСИБО!!!!!!!!!!!!
Обсуждение
03.11.2009, 21:08
общий
это ответ
Здравствуйте, Magma.
Циклическая резонансная частота ωр вынужденных колебаний системы связана с циклической частотой ω0 собственных колебаний системы соотношением
ωр = √(ω02 - 2β2),
следовательно,
2πνр = √(4π2ν02 - 2β2),
νр = √(4π2ν02 - 2β2)/(2π),
νр/ν0 = √(4π2ν02 - 2β2)/(2πν0).
После подстановки в полученную формулу числовых значений величин получаем
νр/ν0 = √(4π2 ∙ (1000)2 – 2 ∙ (400)2)/(2π ∙ 1000) ≈ 0,996,
т. е. резонансная частота колебаний составляет 99,6 % частоты собственных колебаний системы.
Ответ: νр/ν0 ≈ 0,996.
С уважением.
Циклическая резонансная частота ωр вынужденных колебаний системы связана с циклической частотой ω0 собственных колебаний системы соотношением
ωр = √(ω02 - 2β2),
следовательно,
2πνр = √(4π2ν02 - 2β2),
νр = √(4π2ν02 - 2β2)/(2π),
νр/ν0 = √(4π2ν02 - 2β2)/(2πν0).
После подстановки в полученную формулу числовых значений величин получаем
νр/ν0 = √(4π2 ∙ (1000)2 – 2 ∙ (400)2)/(2π ∙ 1000) ≈ 0,996,
т. е. резонансная частота колебаний составляет 99,6 % частоты собственных колебаний системы.
Ответ: νр/ν0 ≈ 0,996.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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