the amplitude of a shm reduces to 1/3 in first 20 second then in first 40 seconds its amplitude becomes - Physics - Oscillations

Question

the amplitude of a shm reduces to 1/3 in first 20 second then in
first 40 seconds its amplitude becomes _ ???

Sanjay Singh · Accepted Answer

Dear student
Amplitude in case of damped simple harmonic motion isA(t)=A0e-bt2m
1Amplitude reduces to A03 in time t=20 sec
Putting in eqn 1A03=A0e-b×202m
213=e-b×202mLet amplitude become A1 after a time 40secA1=A0e-b×402m
3Squaring equation 
2 on both sides19=e-b×402m Putting the value of e-b×402m in eqn 
3A1=A0e-b×402m
A1=A0×19So amplitude reduces to 19 in the first 40 secondsRegards

the amplitude of a shm reduces to 1/3 in first 20 second then in first 40 seconds its amplitude becomes _ ???