In the case of a simple pendulum executing SH | vedclass

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(A) For a simple pendulum,the tension $(T)$ in the string is given by $T = mg \cos 	heta + \frac{mv^2}{L}$.At the mean position,the velocity $v$ is m

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(A) For a simple pendulum,the tension $(T)$ in the string is given by $T = mg \cos 	heta + \frac{mv^2}{L}$.At the mean position,the velocity $v$ is maximum,so the tension $T$ is maximum.At the extreme positions,the velocity $v$ is zero and $	heta$ is maximum,so the tension $T$ is minimum.Since the pendulum executes $SHM$,the displacement $	heta$ varies as $	heta = 	heta_0 \sin(\omega t + \phi)$.The tension $T$ varies with a frequency double that of the pendulum's oscillation frequency because it reaches a maximum twice in one complete oscillation (once at the mean position during the swing in each direction).Since the bob is not at the mean position at $t=0$,the tension starts from an intermediate value and oscillates with a frequency $2f$. The graph shown in option $A$ represents this periodic variation of tension with time.

In the case of a simple pendulum executing $SHM$,at $t=0$,the bob is not at the mean position. The graph drawn between the tension $(T)$ in the string and time $(t)$ is

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