A particle is performing damped oscillation with frequency `5Hz`. After every `10` oscillations its amplitude becmoes half. Find time from beginning after which the amplitude becomes `1//1000` of its initial amplitude :

Options

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

Explanation

Amplitude `A = A _ 0 e ^( -bt// 2m ) `
` (A _ 0 ) /(2) = A_0 e ^( -(b)/(2m )(2)) " " (A _ 0) /( 1000) = A _ 0e ^( ( -b ) /(2m )t ) `
Solving we get , ` t = 20 s `.