For a damped oscillation of a particle, show that time taken for the amplitude to drop to half of its initial value =(2m ln (2))/(b), where b is a damping constant.

For a damped oscillation of a particle, show that time taken for the a

1.	For a damped oscillation of a particle, show that time taken for the amplitude to drop to half of its initial value =(2m ln (2))/(b), where b is a damping constant.
Answer» SOLUTION :Instantaneous displacement of a PARTICLE `=x(t)=Ae^(-bt//2m)COS(OMEGA^(1)t+phi)` Taking `cos(omega.t+phi)=1" for "omega.t+pi=0 and x(t)=(A)/(2)` We get`""(A)/(2)=(A)/(e^(bt//2m))i.e. e^(bt//2m)=2` `therefore""t=(2.303log2)(2m)/(b)=(2m ln 2)/(b)`