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 $T = mg \cos 	heta + \frac{mv^2}{l}$.For small oscillations,$	heta$ is small,s

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(A) For a simple pendulum,the tension $(T)$ in the string is given by $T = mg \cos 	heta + \frac{mv^2}{l}$.For small oscillations,$	heta$ is small,so $\cos 	heta \approx 1 - \frac{	heta^2}{2}$.The velocity $v$ is related to the angular displacement $	heta$ by $v = l \frac{d	heta}{dt}$.Since the pendulum executes $SHM$,$	heta = 	heta_0 \sin(\omega t + \phi)$.Substituting these,we find that $T$ varies with time as $T \propto \cos(2\omega t + 2\phi)$.The frequency of the tension variation is twice the frequency of the pendulum's oscillation.Since the bob is not at the mean position at $t=0$,the phase $\phi 
eq 0$,and the tension will not be at its maximum or minimum value at $t=0$. Graph $(a)$ represents a periodic variation of tension with time,which is consistent with the physical behavior of a pendulum.

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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