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Консультация № 180948
26.11.2010, 04:07
0.00 руб.
26.11.2010, 11:12
0
3
1
Здравствуйте, уважаемые эксперты! Прошу Вас ответить на следующий вопрос:
Затухающие колебания происходят по закону x=0,05e-0,16tsin(8t). Найти амплитуду после 20 колебаний.
Затухающие колебания происходят по закону x=0,05e-0,16tsin(8t). Найти амплитуду после 20 колебаний.
Обсуждение
26.11.2010, 07:57
общий
Здравствуйте, Иван Петрович!
Уточните, пожалуйста, условие: x=0,05e-0,16tsin(8t) или x=0,05e-0,16tsin(8t)?
С уважением.
Уточните, пожалуйста, условие: x=0,05e-0,16tsin(8t) или x=0,05e-0,16tsin(8t)?
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
26.11.2010, 10:57
общий
это ответ
Здравствуйте, Иван Петрович!
Уравнение затухающего колебательного движения имеет вид:
x=A0e-[$948$]tsin([$969$]t+[$966$])
В данной задаче имеем (будем считать все величины даны в СИ):
A0=0,05 м
[$948$]=0,16 с-1
[$969$]=8 рад/с
Все, что стоит перед знаком синуса и есть амплитуда:
A=0.05e-0.16t
Уточним условие задачи и будем считать, что речь идет о 20 полных колебаниях:
T (период) по определению есть время одного полного колебания. Тогда за 20 полных колебаний будем иметь:
t=20*T
Период найдем через циклическую частоту:
T=2п/[$969$]
t=40п/[$969$]
Тогда окончательно имеем:
A=0.05*e-0.16*40п/[$969$]
Вычислим искомую величину:
A=0.05*e-0.16*40*3.14/8[$8776$]0.005 (м)
Будут вопросы обращайтесь в мини-форум.
Удачи
Уравнение затухающего колебательного движения имеет вид:
x=A0e-[$948$]tsin([$969$]t+[$966$])
В данной задаче имеем (будем считать все величины даны в СИ):
A0=0,05 м
[$948$]=0,16 с-1
[$969$]=8 рад/с
Все, что стоит перед знаком синуса и есть амплитуда:
A=0.05e-0.16t
Уточним условие задачи и будем считать, что речь идет о 20 полных колебаниях:
T (период) по определению есть время одного полного колебания. Тогда за 20 полных колебаний будем иметь:
t=20*T
Период найдем через циклическую частоту:
T=2п/[$969$]
t=40п/[$969$]
Тогда окончательно имеем:
A=0.05*e-0.16*40п/[$969$]
Вычислим искомую величину:
A=0.05*e-0.16*40*3.14/8[$8776$]0.005 (м)
Будут вопросы обращайтесь в мини-форум.
Удачи
5
Большое спасибо!!!
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