Oscillations

JEE Main level, single correct, medium

28 of 194

Question 28 of 194

The motion of a simple pendulum executing S.H.M. is represented by the following equation y=Asin⁡(πt+ϕ)y=A\sin \left(\pi t+\phi \right), where time is measured in second. The length of pendulum is

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Answer: (C) 99.4cm99.4cm

Comparing the given equation y=Asin⁡(πt+ϕ)y=A\sin \left(\pi t+\phi \right) with a standard equation y=Asin⁡(ωt+ϕ)y=A\sin \left(\omega t+\phi \right). We have
ω=πrads−1\omega =\pi rad{s}^{-1}
Since time period is T=2πω=2sT=\dfrac{2\pi }{\omega }=2s, it is a second's pendulum.
T=2πLg⇒L=gπ2=99.4cmT=2\pi \sqrt{\dfrac{L}{g}}\Rightarrow L=\dfrac{g}{{\pi }^{2}}=99.4cm

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