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. `2`
B. `1/15"ln"3`
C. `1/2`
D. `1/3"ln"3`

Answer

D

Explanation

Amplitude of pendulum will very as
`A = A_(0)e^(-deltaf), delta =` damping constant
`E = 1/(2)kA^(2) = 1/2 kA_(0)e^(-2deltat)`
`E = E_(0)e^(-2deltat)`
at `t = 0, E_(0) = 45 J` , at `t = 15 s , E = 15 J`
so, `15 = 45 e^(-2delta xx 15) rArr delta = 1/3 ln3`