In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value `a_(0)` at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be

Options

A. A)`(a_(0))/(2)`
B. B)`(a_(0))/(6)`
C. C)`(a_(0))/(12)`
D. D)`(a_(0))/(9)`

Answer

D

Explanation

In damped oscillation, amplitude goes on decaying exponentially
`a=a_(0)e^(-bt)`
where b = damping coefficient.
Initially, `(a_(0))/(3)=a_(0)e^(-bxx100T)`
where T is time of one oscillation.
or `(1)/(3)=e^(-100bT)...(i)`
Finally, `a=a_(0)e^(-bxx200T)`
or `a=a_(0)[e^(-100bT)]^(2)`
or `a=a_(0)xx[(1)/(3)]^(2)` [From Eq. (i)]
or `a=(a_(0))/(9)`