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 ?

Options

A. `(1)/(5)`
B. `(2)/(3)`
C. `(1)/(6)`
D. `(1)/(9)`

Answer

D

Explanation

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)`