The amplitude of a damped oscillator decreases to `0.9` times ist oringinal magnitude in `5s`, In anothet `10s` it will decrease to α times its original magnitude, where α equals to .

Options

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

Answer

C

Explanation

`A(t)=A_(0)e^(-b//2m)`
`A(5)=0.9A_(0)`
`0.9A_(0)=A_(0)e^(-b(5)//2m)`
`A(15)=alphaA_(0)`
`alphaA_(0)=A_(0)e^(-b(15)//2m)`
`impliesalpha=(0.9)^(3)=0.729`