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Консультация № 196526
01.10.2019, 12:01
0.00 руб.
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1
Здравствуйте! Прошу помощи в следующем вопросе:
Найти параметры волн, которые при сложении дают колебание Asin(t)cos(33t)
Найти параметры волн, которые при сложении дают колебание Asin(t)cos(33t)
Обсуждение
02.10.2019, 20:38
общий
это ответ
Здравствуйте, dar777!
Дано: x(t)=Asin(t)cos(33t) -- уравнение результирующего колебания.
Определить: A1, A2; [$969$]1, [$969$]2; ([$966$]0)1, ([$966$]0)2 -- соответственно амплитуды, циклические частоты и начальные фазы составляющих колебаний.
Решение
Воспользуемся формулой
При [$945$]=t, [$946$]=33t получим
(здесь мы учли, что sin(-[$945$])=-sin[$945$] [1, с. 22], sin([$945$]+[$960$])=-sin[$945$] [1, с. 34]), или
где x1(t)=A/2*sin(32t+[$960$]), x2(t)=A/2*sin(34t); следовательно, A1=A2=A/2; [$969$]1=32, [$969$]2=34; ([$966$]0)1=[$960$], ([$966$]0)2=0.
Ответ: A1=A2=A/2; [$969$]1=32, [$969$]2=34; ([$966$]0)1=[$960$], ([$966$]0)2=0.
Литература
1. Новосёлов С. И. Тригонометрия. Учебник для 9 -- 10 классов средней школы. -- М.: Госучпедгиз РСФСР, 1961. -- 96 с.
Дано: x(t)=Asin(t)cos(33t) -- уравнение результирующего колебания.
Определить: A1, A2; [$969$]1, [$969$]2; ([$966$]0)1, ([$966$]0)2 -- соответственно амплитуды, циклические частоты и начальные фазы составляющих колебаний.
Решение
Воспользуемся формулой
sin[$945$]*cos[$946$]=1/2*(sin([$945$]-[$946$])+sin([$945$]+[$946$])) [1, с. 38].
При [$945$]=t, [$946$]=33t получим
Asin(t)cos(33t)=A/2*(sin(t-33t)+sin(t+33t))=A/2*(sin(-32t)+sin(34t))=A/2*(-sin(32t)+sin(34t))=
=A/2*(sin(32t+[$960$])+sin(34t))=A/2*sin(32t+[$960$])+A/2*sin(34t)
(здесь мы учли, что sin(-[$945$])=-sin[$945$] [1, с. 22], sin([$945$]+[$960$])=-sin[$945$] [1, с. 34]), или
x(t)=x1(t)+x2(t),
где x1(t)=A/2*sin(32t+[$960$]), x2(t)=A/2*sin(34t); следовательно, A1=A2=A/2; [$969$]1=32, [$969$]2=34; ([$966$]0)1=[$960$], ([$966$]0)2=0.
Ответ: A1=A2=A/2; [$969$]1=32, [$969$]2=34; ([$966$]0)1=[$960$], ([$966$]0)2=0.
Литература
1. Новосёлов С. И. Тригонометрия. Учебник для 9 -- 10 классов средней школы. -- М.: Госучпедгиз РСФСР, 1961. -- 96 с.
5
Это самое лучшее решение!
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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