Question

The amplitude of a damped oscillator becomes `(1)/(27)^(th)` of its initial value after `6` minutes. Its amplitude after `2` minutes is
A. `(A_(0))/(3)`
B. `(A_(0))/(9)`
C. `(A_(0))/(54)`
D. `(A_(0))/(81)`

Answer 1

Correct Answer - A
For damped oscillator `A = A_(0)^(-bt)`
Here `(A_(0))/(27) = A_(0)e^(-6b), A_(2) = A_(0)e^(-2b) = A_(0) [e^(-6b)]^((1)/(3))`