JEE Main 2015 · 11 Apr · Shift 1 · Physics Q12

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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, its damping constant (in s $^{-1}$ ) is :

\dfrac1{30}\ln3

\dfrac1{15}\ln3

\dfrac12

Answer and worked solution

Official answer: B

Take $E=E_0e^{-bt}$ . In 15 oscillations ( $t=15$ s) the energy falls from 45 J to 15 J:
$e^{-15b}=\frac13\implies b=\frac{\ln3}{15}\text{ s}^{-1}.$

Topics:Damped and forced oscillations

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JEE Main 2015 · 11 Apr · Shift 1, Physics question 12