The amplitude of damped oscillator decreased to `0.9` times its original magnitude is `5s`. In another `10s` it will decrease to `alpha` times its original magnitude, where `alpha` equals.

Options

A. `0.7`
B. `0.81`
C. `0.729`
D. `0.6`

Answer

C

Explanation

`A = A_(0)e^(-(b(5))/(2m))`
after `5` second
`0.9A_(0) = A_(0)ɵ^(-(b(5))/(2m)) …..(i)`
After `10` more second
`A = A_(0)ɵ^(-(b(5))/(2m)) ….. (ii)`
From `(i)` and `(ii)`
`A = 0.729 A_(0)`