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. 0.81
B. 0.729
C. 0.6
D. 0.7

Answer

B

Explanation

The amplitude of a damped oscillator at a given instant of time t is given by `A=A_(0)e^(-bt//2m)`
Where is its amplitude in the absence of damping, b is the damping constant.
As per question
After 5s (i.e. t = 5 s), its amplitude becomes 0.9A
`implies 0.9=e^(-5b//2m)`.......(i)After 10 more second (i.e. t = 15 s), its amplitude becomes
`alphaA_(0)=A_(0)e^(-b(15)//2m)= A_(0)e^(15b//2m)`
`alpha=e^((15b//2m)^(3))=(0.9)^(3)` (using(i))
=0.729.