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If the speed $(v)$ of the bob in a simple pendulum is plotted against the tangential acceleration $(a)$, the correct graph will be represented by -
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I
In SHM
$\mathrm{a}=-\omega^{2} \mathrm{x}$
$\begin{array}{l}
\mathrm{v}=\omega \sqrt{\mathrm{A}^{2}-\mathrm{x}^{2}} \\
\mathrm{v}^{2}=\omega^{2}\left(\mathrm{~A}^{2}-\mathrm{x}^{2}\right) \\
\mathrm{v}^{2}=\omega^{2} \mathrm{~A}^{2}-\omega^{2} \times \frac{\mathrm{a}^{2}}{\omega^{2}} \\
\mathrm{v}^{2}+\frac{\mathrm{a}^{2}}{\omega^{2}}=\omega^{2} \mathrm{~A}^{2} \\
\frac{\mathrm{v}^{2}}{\omega^{2} \mathrm{~A}^{2}}+\frac{\mathrm{a}^{2}}{\omega^{4} \mathrm{~A}^{2}}=1
\end{array}$
i.e. ellipse
$\mathrm{a}=-\omega^{2} \mathrm{x}$
$\begin{array}{l}
\mathrm{v}=\omega \sqrt{\mathrm{A}^{2}-\mathrm{x}^{2}} \\
\mathrm{v}^{2}=\omega^{2}\left(\mathrm{~A}^{2}-\mathrm{x}^{2}\right) \\
\mathrm{v}^{2}=\omega^{2} \mathrm{~A}^{2}-\omega^{2} \times \frac{\mathrm{a}^{2}}{\omega^{2}} \\
\mathrm{v}^{2}+\frac{\mathrm{a}^{2}}{\omega^{2}}=\omega^{2} \mathrm{~A}^{2} \\
\frac{\mathrm{v}^{2}}{\omega^{2} \mathrm{~A}^{2}}+\frac{\mathrm{a}^{2}}{\omega^{4} \mathrm{~A}^{2}}=1
\end{array}$
i.e. ellipse
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