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For a damped oscillator which follow the...


For a damped oscillator which follow the equation `vecF=-kvecx-bvecV`
the mass of the block is 100 gm K=100N/M and the damping constant is 20 gm/sec. thhen find the time taken for its mechanical energy to drop to one-fourth of its initial value.

A

1.73

B

3.46

C

6.93

D

13.84

Text Solution

Verified by Experts

The correct Answer is:
C
`E=(1)/(2)KA^(2)-(bt//m)`
`therefore(1)/(4)=(E(t=t))/(E(t=0))=e^(-bt//m)`
taking log and solving we get `t=(2xx0.963)/(b//m)=6.93sec`
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