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Задать вопрос экспертам

Консультация № 182669

30.03.2011, 00:46

52.36 руб.

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Образование

Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
складываются два гармоничных колебания одного направления, описываемые уравнениями
x1 = 3cos2[$8719$]t, см и

x2 =3cos( 2[$8719$]t + [$8719$][$247$]4), см.
Определить для результатирующего колебания амплитуду и начальную фазу. Записать уравнение для результатирующего колебания и представить векторную диаграмму сложения амплитуд.

Обсуждение

давно

Киселев Виталий Сергеевич

Академик
324866
619

30.03.2011, 07:11

общий

это ответ

Здравствуйте, Посетитель - 364448!

x₁=A₁cos([$969$]t+[$966$]₁)
x₂=A₂cos([$969$]t+[$966$]₂)
[$969$]=2п
A₁=A₂=3 (см)
[$966$]₁=0
[$966$]₂=п/4
[$916$][$966$]=[$966$]₂ - [$966$]₁
x=Acos([$969$]t+[$966$])
tg[$966$]=(A₁sin[$966$]₁+A₂sin[$966$]₂)/(A₁cos[$966$]₁+A₂cos[$966$]₂)=(sin[$966$]₁+sin[$966$]₂)/(cos[$966$]₁+cos[$966$]₂)
A=[$8730$](A₁²+A₂²+2A₁A₂cos[$916$][$966$])=A₁[$8730$][2(1+cos[$916$][$966$])]
Вычислим искомые величины:
tg[$966$]=(sin(0)+sin(п/4))/(cos(0)+cos(п/4))=0.414
[$966$]=п/8
A=0.03[$8730$][2(1+cos(п/4))]=5.54 (см)
x=5.54cos(2пt+п/8) (см)
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