A pendulum with time period of 1s is losing energy due to damping. At certain time its energy is 45 J. If after completing 15 oscillations, its energy has become 15 J, itsdamping 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`