The amplitude of a damped oscillator becomes `((1)/(3))` rd in 2s. If its amplitude after 6 s is `(1)/(n)` times the original amplitude, the value of n is

Options

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

Answer

D

Explanation

We have
`A = A_(0)e^(-bt//2m)`
In this case after 6s amplitudes becomes `(1)/(27)` times.