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. (a) `0.7`
B. (b) `0.81`
C. (c ) `0.729`
D. (d) `0.6`

Answer

C

Explanation

(c ) :. `A=A_(0)e^b_(t)/2_(m)` (where, `A_(0)=maximum amplitude)`
According to the questions, after 5 second,
`0.9A_(0)e^((b(15)/2_(m)`
From eq^(n)s (i) and (ii)`
`A=0.729 A_(0) :. `a=0.729`.