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

Options

A. 100s
B. 10s
C. 50s
D. 20s

Answer

D

Explanation

Amplitude `A=A_(0)e^(-bt//2m)`
`A_(0)/(2)=A_(0)e^(-b/(2m)(2))`, `A_(0)/1000=A_(0)e^(-b/(2m)tau)`
Solving we get, `tau`=20s.