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  4. The motion of a simple pendulum excuting S.H.M. is represented by following equation. Y = A sin (π t +φ), where time is measured in second. The length of pendulum is :

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Q. The motion of a simple pendulum excuting S.H.M. is represented by following equation. $Y = A \sin (\pi t +\phi)$, where time is measured in second. The length of pendulum is :

JEE MainJEE Main 2022Oscillations

Solution:

$\omega=\sqrt{\frac{ g }{\ell}}=\pi$
$\frac{ g }{\ell}=\pi^{2} \Rightarrow \ell=\frac{ g }{\pi^{2}}$
$\ell=\frac{980}{\pi^{2}} \approx 99.4\, cm$