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(B) For a particle in $SHM$,its velocity $v$ depends on displacement $x$ as:$v = \omega \sqrt{A^{2} - x^{2}}$Where $\omega$ is the angular frequency a

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Elliptical

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(B) For a particle in $SHM$,its velocity $v$ depends on displacement $x$ as:$v = \omega \sqrt{A^{2} - x^{2}}$Where $\omega$ is the angular frequency and $A$ is the amplitude.Squaring both sides,we get:$v^{2} = \omega^{2} (A^{2} - x^{2})$$v^{2} = \omega^{2} A^{2} - \omega^{2} x^{2}$Rearranging the terms:$v^{2} + \omega^{2} x^{2} = \omega^{2} A^{2}$Dividing by $\omega^{2} A^{2}$:$\frac{v^{2}}{(\omega A)^{2}} + \frac{x^{2}}{A^{2}} = 1$This equation is of the form $\frac{y^{2}}{b^{2}} + \frac{x^{2}}{a^{2}} = 1$,which represents an ellipse.Therefore,the graph between velocity $v$ and displacement $x$ is elliptical.

When a particle executes simple harmonic motion,the nature of the graph of velocity as a function of displacement will be:

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