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Консультация № 201724
20.11.2021, 22:12
0.00 руб.
21.11.2021, 23:22
0
3
1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Уравнение незатухающих колебаний дано в виде: Y=cos0,5[$960$]t мм. Найти смещение и скорость колеблющейся точки, отстоящей от источника на расстоянии 250 м, в момент времени t=1,5 с. Длина волны равна 1000 м.
Уравнение незатухающих колебаний дано в виде: Y=cos0,5[$960$]t мм. Найти смещение и скорость колеблющейся точки, отстоящей от источника на расстоянии 250 м, в момент времени t=1,5 с. Длина волны равна 1000 м.
Обсуждение
21.11.2021, 08:02
общий
Адресаты:
ivgtrk Y=cos0,5?t
Сообщите, пожалуйста, что обозначает символ вопроса в этом выражении?
Об авторе:
Facta loquuntur.
Facta loquuntur.
21.11.2021, 11:02
общий
Гордиенко Андрей Владимирович что обозначает символ вопроса в этом выражении
Здравствуйте. Это пи
21.11.2021, 23:06
общий
21.11.2021, 23:12
это ответ
Дано:
у=cos(([$960$]/2)*t) (мм)
x1=250 м
t1=1,5 с
[$955$] = 1000 м
Найти: y1; v1
Решение:
Расстояние от начала координат до точки А с координатами хА=250 м и уА=0 равно четверти длины волны:
(хА=[$955$]/4 = 250 м).
Следовательно, колебания точки А будут происходить со сдвигом по фазе равным [$966$]=-[$960$]/2 относительно колебаний источника волны.
уА=cos(([$960$]/2)*t-[$960$]/2) (мм)
или
уА=-sin(([$960$]/2)*t) (мм) - уравнение колебаний точки А.
Тогда, через t1=1,5 с
уА1=-sin(([$960$]/2)*3/2) = -sin((3/4)*[$960$])(мм) = -([$8730$]2)/2 мм [$8776$] -0,7 мм
Далее
Скорость - производная координаты по времени, следовательно
vA(t)=y'A(t) = -A*[$969$]*cos([$969$]*t)
vA1=-1мм*([$960$]/2)с-1*cos(([$960$]/2)*3/2) = -1,57*cos(3*[$960$]/4)мм/с=-1,57*[$8730$]2/2 мм/с [$8776$] 1,1 мм/с
Удачи
у=cos(([$960$]/2)*t) (мм)
x1=250 м
t1=1,5 с
[$955$] = 1000 м
Найти: y1; v1
Решение:
Расстояние от начала координат до точки А с координатами хА=250 м и уА=0 равно четверти длины волны:
(хА=[$955$]/4 = 250 м).
Следовательно, колебания точки А будут происходить со сдвигом по фазе равным [$966$]=-[$960$]/2 относительно колебаний источника волны.
уА=cos(([$960$]/2)*t-[$960$]/2) (мм)
или
уА=-sin(([$960$]/2)*t) (мм) - уравнение колебаний точки А.
Тогда, через t1=1,5 с
уА1=-sin(([$960$]/2)*3/2) = -sin((3/4)*[$960$])(мм) = -([$8730$]2)/2 мм [$8776$] -0,7 мм
Далее
Скорость - производная координаты по времени, следовательно
vA(t)=y'A(t) = -A*[$969$]*cos([$969$]*t)
vA1=-1мм*([$960$]/2)с-1*cos(([$960$]/2)*3/2) = -1,57*cos(3*[$960$]/4)мм/с=-1,57*[$8730$]2/2 мм/с [$8776$] 1,1 мм/с
Удачи
5
Благодарю!
Об авторе:
С уважением
shvetski
С уважением
shvetski
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