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)ln3`
C. 2
D. `(1)/(15)ln3`

Answer

D

Explanation

As we know, `E=E_(0)e^((bt)/(m))" "15=45e^(-(b15)/(m))`
[As no. of oscillations = 15 so t = 15 sec]
`(1)/(3)=e^(-(b15)/(m))`
Taking log on both sides `(b)/(m)=(1)/(15)"l n 3"`