A pendulum with time period of $1\, s$ is losing energy due to damping. At certain time its energy is $45\, J$. If after completing $15\,oscillations$ , its energy has become $15\, J$, its damping constant (in $s^{-1}$ ) is
JEE MAIN 2015, Medium
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As we know, $E=E_{0} e^{-\frac{b t}{m}}$
$15=45 e^{-\frac{b 15}{m}}$
[As no. of oscillations $=15 \text { so } t=15 \mathrm{sec}]$
$\frac{1}{3}=e^{-\frac{b 15}{m}}$
Taking log on both sides
$\frac{b}{m}=\frac{1}{15} \ell \mathrm{n} 3$
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