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) 100s
(C) 50s (D) 20s
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A=A0e−γt
A=2A0 after 10 oscillations
∵ After 2 seconds
2A0=A0e−γ(2)
2=e2γ
ℓn2=2γ
γ=2ℓn2
∵A=A0e−γt
ℓnAA0=γt
ℓn1000=2ℓn2t
2(ℓn23ℓn10)=t
ℓn26ℓn10=1
t=19.931sec
t = 20sec
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