The amplitude of a damped oscillation decreases to 0.8 times its original magnitude in 4s. In another 12s, it will decrease to n time its original magnitude. Find the value of n.

Explanation

The amplitude of the dampled oscillation at an instant t is given by
`a=a_(0)e^(-bt//2m)`
When `t=4s, a=0.8 a_(0), then `
`0.8a_(0)=a_(0)e^(-bxx4//2m)or 0.8=e^(-4b//2m)` …(i)
When `t=4+12=16s, a=na_(0), ` then
`na_(0)=a_(0)e^(-bxx16//2m)or n=e^(-16b//2m)`
or `n=(e^(-4b//2m))^(4)=(0.8)^(4)=0.4096`