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Консультация № 200372
03.03.2021, 16:54
0.00 руб.
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Здравствуйте! Прошу помощи в следующем вопросе:
В момент времени t = 2T от начала колебаний амплитуда равна 20 см, а в момент времени t = 4T она равна 18 см. Частота равна 0,5 Гц.
Найти:
0) логарифмический декремент затухания;
1) коэффициент затухания;
2) амплитуду в момент времени t = 9T (в см);
3) амплитуду в момент времени t = 0 (в см).
В момент времени t = 2T от начала колебаний амплитуда равна 20 см, а в момент времени t = 4T она равна 18 см. Частота равна 0,5 Гц.
Найти:
0) логарифмический декремент затухания;
1) коэффициент затухания;
2) амплитуду в момент времени t = 9T (в см);
3) амплитуду в момент времени t = 0 (в см).
Обсуждение
07.03.2021, 10:59
общий
это ответ
Здравствуйте, gleb.babin!
Дано:
t1=2T
A1=20см
t2=4T
A2=18см
f=0,5 Гц
t3=9T
Найти:
0) [$967$];
1) [$946$];
2) А3 (в см);
3) Ао (в см)
Решение:
1. Период колебаний
T=1/f = 1/0,5 = 2 c;
2. Амплитуда затухающих колебаний
A=Aoe-[$946$]t (1)
Тогда
A1=Aoe-[$946$]t[sub]1[/sub]
A2=Aoe-[$946$]t[sub]2[/sub]
---
20=Aoe-[$946$]*2T
18=Aoe-[$946$]*4T
---
20/18=e4[$946$]
ln(20/18)=4[$946$]
[$8658$]
Коэффициент затухания
[$946$]=0,026 c-1
----
Логарифмический декремент затухания
[$967$]=[$946$]T (2)
[$967$]=0,052
---
Из формулы (1)
Ao=A1*e[$946$]t[sub]1[/sub] (3)
Ao=20*e4[$946$] = 22,2 cм [$8776$] 22 см
---
Согласно (1)
А3=22,2*e-0.026*18=13,9 см[$8776$]14 см
---
Удачи
Дано:
t1=2T
A1=20см
t2=4T
A2=18см
f=0,5 Гц
t3=9T
Найти:
0) [$967$];
1) [$946$];
2) А3 (в см);
3) Ао (в см)
Решение:
1. Период колебаний
T=1/f = 1/0,5 = 2 c;
2. Амплитуда затухающих колебаний
A=Aoe-[$946$]t (1)
Тогда
A1=Aoe-[$946$]t[sub]1[/sub]
A2=Aoe-[$946$]t[sub]2[/sub]
---
20=Aoe-[$946$]*2T
18=Aoe-[$946$]*4T
---
20/18=e4[$946$]
ln(20/18)=4[$946$]
[$8658$]
Коэффициент затухания
[$946$]=0,026 c-1
----
Логарифмический декремент затухания
[$967$]=[$946$]T (2)
[$967$]=0,052
---
Из формулы (1)
Ao=A1*e[$946$]t[sub]1[/sub] (3)
Ao=20*e4[$946$] = 22,2 cм [$8776$] 22 см
---
Согласно (1)
А3=22,2*e-0.026*18=13,9 см[$8776$]14 см
---
Удачи
Об авторе:
С уважением
shvetski
С уважением
shvetski
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