The amplitude of a damped oscillator decreases to `0/9` times ist oringinal magnitude in `5s`, In anothet `10s` it will decrease to a times its original magnitude, wherea eqcrease .

Options

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

Answer

C

Explanation

Amplitude of damped oscillation
`a=a_(0)e^(-bt//2m)`
As, `a=0.90 a_(0), t=5s,` so
`0.9 a_(0)=a_(0) e^(-bt//2m)` or ` 0.9=e^(-5b//2m` …(i)
When `t=5+10=15s, a=xa_(0), ` then
`xa_(0)=a_(0)e^(-bxx15//2m)`
or `x=[e^(-5b//2m)]^(3)=(0.9)^(3)=0.729`