The amplitude of a damped oscillator becomes `(1)/(27)^(th)` of its initial value after `6` minutes. Its amplitude after `2` minutes is

Options

A. `(A_(0))/(3)`
B. `(A_(0))/(9)`
C. `(A_(0))/(54)`
D. `(A_(0))/(81)`

Answer

A

Explanation

`A = A_(0) e^(-vt)`
`(A_(0))/(27) = A_(0)e^(-v(6)) rArr e^(-6v) = (1)/(27)`
After 2 min, `A = A_(0)e^(-v(2))`
`A = (A_(0))/(3)`