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Question

Equation F=bvkx represents equation of a damped oscillation for a particle of 2 kg mass where b=ln2N.S.m and k=100N/m then time after which energy of oscillations will be reduced to half of initial is :

A
ln 2 sec
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B
2 sec
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C
2 ln 2 sec
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D
1 sec
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Solution

The correct option is B 2 sec
For damped oscillation for a particle of m=2 .
F=bVkx
Amplitude ca be written as A=A0ebt2m
Energy EA2
Energy E=E0ebtm
Let after time t0 its energy becomes half of initial energy.
E02=E0ebt0m
ln2=bt0m
t0=m×ln2b
t0=2×ln2ln2=2sec
t0=2sec

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