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In damped oscillations damping froce is ...

In damped oscillations damping froce is directly proportional to speed of ocillatior .If amplitude becomes half to its maximum value is 1 s, then after 2 s amplitude will be (`A_(0)`- initial amplitude)

A

`(1)/(4)A_(0)`

B

`(1)/(2)A_(0)`

C

`A_(0)`

D

`(sqrt(3)A_(0))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
(a) Amplitude of damped oscillation is `A=A_(0)e^(-gammat)`
`A=(A_(0))/(2)`
where t=1s
So, `(A_(0))/(2)=A_(0)e^(-gamma1)` or `e^(gamma)=2`
After 2 s, `A=A_(0)e^(-gamma^(3))implies A=(A_(0))/(4)`
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