(D) For a simple pendulum,the angular acceleration $\alpha$ is given by the equation $\alpha = -\omega^2 \theta$,where $\omega^2 = \frac{g}{l}$.Since

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(D) For a simple pendulum,the angular acceleration $\alpha$ is given by the equation $\alpha = -\omega^2 \theta$,where $\omega^2 = \frac{g}{l}$.Since the angular accelerations are equal in magnitude,we have $|\alpha_1| = |\alpha_2|$.Substituting the expression for $\alpha$,we get $\frac{g}{l_1} \theta_1 = \frac{g}{l_2} \theta_2$.Canceling the acceleration due to gravity $g$ from both sides,we obtain $\frac{\theta_1}{l_1} = \frac{\theta_2}{l_2}$.Rearranging the terms,we get $\theta_1 l_2 = \theta_2 l_1$.

Class 11 Physics Oscillations SHM of Simple Pendulum

Medium

Two simple pendulums having lengths $l_1$ and $l_2$ with negligible string mass undergo angular displacements $\theta_1$ and $\theta_2$ from their mean positions,respectively. If the angular accelerations of both pendulums are same,then which expression is correct?

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A
$\theta_1 l_2^2 = \theta_2 l_1^2$
B
$\theta_1 l_1 = \theta_2 l_2$
C
$\theta_1 l_1^2 = \theta_2 l_2^2$
D
$\theta_1 l_2 = \theta_2 l_1$

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Two simple pendulums having lengths $l_1$ and $l_2$ with negligible string mass undergo angular displacements $\theta_1$ and $\theta_2$ from their mean positions,respectively. If the angular accelerations of both pendulums are same,then which expression is correct?

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$A$ simple pendulum oscillates in a vertical plane. When it passes through the mean position,the tension in the string is $3$ times the weight of the pendulum bob. What is the maximum displacement of the pendulum string with respect to the vertical in degrees?

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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 .............$cm$.

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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 .............$cm$.