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A damped harmonic oscillator has a frequ...

A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to `1/1000` of the original amplitude is close to:

Text Solution

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Time of half the amplitude is =2s
Using `A=A_(0)e^(-kt)`
`(A_(0))/2=A_()e^(-kxx2)`……….i
and `(A_(0))/1000=A_(e)e^(-kt)` ………..ii
Dividn I and ii and solving, we get
t=20s
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