When a damped harmonic oscillator completes 100 oscillations, its amplitude is reduced to (1)/(3) of its initial value. What will be its amplitude when it completes 200 oscillations ?

When a damped harmonic oscillator completes 100 oscillations, its ampl

1.	When a damped harmonic oscillator completes 100 oscillations, its amplitude is reduced to (1)/(3) of its initial value. What will be its amplitude when it completes 200 oscillations ?
Answer» `(1)/(5)` `(2)/(3)` `(1)/(6)` `(1)/(9)` Solution :In damped vibration, amplitude at any instant t is `a=a_(0)e^(-bt)` If, `t=100 T and a=(a_(0))/(3)` `THEREFORE (a_(0))/(3)=a_(0)e^(-100bT)` If, `t=200 T` `a=a_(0)e^(-bt)=a_(0)e^(-b(200T))` `=a_(0)(e^(-1006T))^(2)` `a=a_(0)((1)/(3))^(2)` `a=(a_(0))/(9)`