A pendulum with time period of `1s` is losing energy due to damping. At time its energy is `45 J`. If after completing `15` oscillations, its energy has become `15 J`. Its damping constant (in `s^(-1)`) is :-

Options

A. `(1)/(2)`
B. `(1)/(30)` In 3
C. `2`
D. `(1)/(15)` In 3

Answer

D

Explanation

The mechanical energy of damped oscillation is
`E = (1)/(2)k(Ae^(-(bt)/(2m)))^(2)`
`rArr" "E=((1)/(2)kA^(2))e^(-(bt)/(m))rArr 15 = 45 e^(-(b xx (15 xx 1))/(m))`
`rArr" "e^((15b)/(m))= 3 rArr (15 b)/(m) log_(e)e=log 3`
So, damping constant `= (b)/(m) = (1)/(15)log_(e)3`
`=(1)/(15)"In 3"" "[because (b)/(m)"is in s"^(-1)]`