A simple pendulum with length L and mass m of | vedclass

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(B) The tension $T$ in the string at the lowest point is given by $T - mg = \frac{mv^2}{L}$,where $v$ is the velocity at the lowest point.For a simple

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$mg\left[ {1 + {{\left( {\frac{A}{L}} \right)}^2}} \right]$

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(B) The tension $T$ in the string at the lowest point is given by $T - mg = \frac{mv^2}{L}$,where $v$ is the velocity at the lowest point.For a simple pendulum,the maximum velocity $v_{\max} = A\omega$,where $\omega = \sqrt{\frac{g}{L}}$.Thus,$v_{\max}^2 = A^2\omega^2 = A^2 \left(\frac{g}{L}\right)$.Substituting this into the tension equation:$T_{\max} = mg + \frac{m(A^2 g/L)}{L} = mg + \frac{mgA^2}{L^2}$.Factoring out $mg$,we get $T_{\max} = mg \left[ 1 + \left( \frac{A}{L} \right)^2 \right]$.

Column-$I$	Column-$II$
$(a)$ $T^2 \to l$	$(i)$ Linear
$(b)$ $T^2 \to g$	$(ii)$ Parabolic
$(c)$ $T \to l$	$(iii)$ Hyperbolic

$A$ simple pendulum with length $L$ and mass $m$ of the bob is vibrating with an amplitude $A$. The maximum tension in the string is

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In the following table, the relation of the graph in column-$I$ and the shape of the graph in column-$II$ is shown. Match them appropriately.
Column-$I$ Column-$II$
$(a)$ $T^2 \to l$ $(i)$ Linear
$(b)$ $T^2 \to g$ $(ii)$ Parabolic
$(c)$ $T \to l$ $(iii)$ Hyperbolic

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