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 .

Explanation

`A = A_(0)e^(-bt//2m)` after `5sec 0.9 = e^(-5b//2m)`
After `10` more sec (i.e., `t = 15sec)` its amplitude becomes `alpha A_(0)`.
Hence, `alphaA_(0) = A_(0)e^(-b(15)//2m) = A_(0)e^(-15b//2m)`
or `alpha = e^(-15b//2m) = (e^(-5b//2m))^(3) = (0.9)^(3) = 0.729`.