The motion of a simple pendulum executing S.H | vedclass

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(C) The standard equation for $S.H.M.$ is $Y = A \sin(\omega t + \phi)$.Comparing this with the given equation $Y = A \sin(\pi t + \phi)$,we get the a

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$99.4$

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(C) The standard equation for $S.H.M.$ is $Y = A \sin(\omega t + \phi)$.Comparing this with the given equation $Y = A \sin(\pi t + \phi)$,we get the angular frequency $\omega = \pi \, rad/s$.For a simple pendulum,the angular frequency is given by $\omega = \sqrt{\frac{g}{\ell}}$.Squaring both sides,we get $\omega^2 = \frac{g}{\ell}$,which implies $\ell = \frac{g}{\omega^2}$.Using the value of acceleration due to gravity $g = 980 \, cm/s^2$ and $\omega = \pi \, rad/s$:$\ell = \frac{980}{\pi^2} \approx \frac{980}{9.8696} \approx 99.3 \, cm$.Rounding to the nearest option,we get $\ell \approx 99.4 \, cm$.

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

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