In damped oscillations, damping force is directly proportional to the speed of the oscillator. If amplitude becomes half of its initial value in 1s, then after 2 s, amplitude will be:
[A0 is initial amplitude]
A
14A0
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B
12A0
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C
A0
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D
√3A02
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Solution
The correct option is A14A0 We know that,
Amplitude of damped oscillation (A)=A0e−γt
As A=A02 at t=1s
So, A02=A0e−γ
or er=2...(i)
After two seconds, A=A0e−2γ A=A0(eγ)−2
Using (1), we get A=A04