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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:

A

10s

B

50s

C

20s

D

100s

Text Solution

Verified by Experts

The correct Answer is:
C
`f = 5 `
So, T = 1/5
10 T = 10 /5 = 2
`A_(0) // 1000 = A_(0) (1//2) ^(t//20`
`(2)^(t//2) = 1000`
`(t//2) log 2 = 3 rArr t = (6)/(log 2) ~~ 20 s `
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