The amplitude of damped oscillator becomes `1/3` in `2s`. Its amplitude after `6s` is `1//n` times the original. The value of `n` is

Options

A. `3^(2)`
B. `root3(3)`
C. `2^(3)`
D. `3^(3)`

Answer

A

Explanation

Amplitude of a damped oscillator at any instant t is `A=A_(0)e^(-bt//2m)`, where `A_(0)` is the original amplitude.
When `t=2s,A=(A_(0))/(3)`
`therefore (A_(0))/(3)=A_(0)e^(-2b//2m)or(1)/(3)=e^(-b//m)" "...(i)`
When `t=6s,A=(A_(0))/(n) therefore (A_(0))/(n)=A_(0)e^(-6b//2m)`
or `(1)/(n)=e^(-3b//m=(e^(-b//m))^(3))=((1)/(3))^(3)therefore n=3^(3)` (Using (i))