The amplitude of damped oscillator decreased to `0.9` times its original magnitude is `5s`. In another `10s` it will decrease to `alpha` times its original magnitude, where `alpha` equals.

Options

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

Answer

A

Explanation

`A=A_0e^(-(bt)/(2m))`
After 5 second
`0.9A_0=A_0e^(-(b(5))/(2m)).......(i)`
After 10 more second
`A=A_0e^(-(b(15))/(2m)" "....(ii)`
From (i) and (ii)
`A= 0.729 A_0`