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

A pendulum with the time period of $1s$ is losing energy due to damping. At a certain time, its energy is $45J$ . If after completing $15$ oscillations its energy has become $15J$ , then its damping constant (in ${s}^{- 1}$ ) will be

Options

A $\dfrac{1}{2}$
B $\dfrac{1}{15}\ln 3$
C $\dfrac{1}{30}\ln 3$
D $2$

Correct answer

C. $\dfrac{1}{30}\ln 3$

Step-by-step solution

Energy of a damping oscillator is&

E = {E}_{0}e^{-2 \gammat}

at time

t

~where

\gamma =

damping constant,~

{E'}^{} = {E}_{o}e^{- 2\gammat}⇒ 15 = 45e^{- 2\gamma\left(15\right)}⇒ \gamma = \dfrac{1}{30}\ln ( 3 )

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