Q.

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

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a

50 s

b

36 s

c

20 s

d

45 s

answer is C.

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Detailed Solution

amplitude of damped oscillation =A=A0e-bt---(1) after 10 seconds A=A02 ⇒A02=A0e-b2 log2=2b b=log22---(2) from equation (1) logA0A=bt     substitute eqn(1) log 1000=log22t t=23log10log2 t=19.93≃20second
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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