Oscillations

JEE Main level, single correct, medium

177 of 194

Question 177 of 194

A pendulum with the time period of 1s1s is losing energy due to damping. At a certain time, its energy is 45J45J. If after completing 1515 oscillations its energy has become 15J15J, then its damping constant (in s−1{s}^{-1}) will be

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Answer: (C) 130ln⁡⁡3\dfrac{1}{30}\ln ⁡3

Energy of a damping oscillator is E=E0e−2γtE={E}_{0}{e}^{-2\gamma t} at time tt where γ=\gamma =damping constant, E′=Eoe−2γt{E'}^{}={E}_{o}{e}^{-2\gamma t}⇒15=45e−2γ(15)\Rightarrow 15=45{e}^{-2\gamma \left(15\right)}⇒γ=130ln⁡(3)\Rightarrow \gamma =\dfrac{1}{30}ln⁡(3)

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