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

A pendulum with time period of `1s` is losing energy due to damping. A

1.	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 :-A. `2`B. `1/15"ln"3`C. `1/2`D. `1/3"ln"3`
Answer» Correct Answer - D 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`

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

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