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(D) In simple harmonic motion $(S.H.M.)$,the displacement $y$ is given by $y = a \sin(\omega t)$ and velocity $v$ is given by $v = a \omega \cos(\omeg

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An ellipse

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(D) In simple harmonic motion $(S.H.M.)$,the displacement $y$ is given by $y = a \sin(\omega t)$ and velocity $v$ is given by $v = a \omega \cos(\omega t)$.From these equations,we can write $\sin(\omega t) = \frac{y}{a}$ and $\cos(\omega t) = \frac{v}{a \omega}$.Using the trigonometric identity $\sin^2(\omega t) + \cos^2(\omega t) = 1$,we get:$\frac{y^2}{a^2} + \frac{v^2}{a^2 \omega^2} = 1$.This is the standard equation of an ellipse in the $(y, v)$ plane,where $y$ is the displacement and $v$ is the velocity.

The graph between velocity and displacement of a particle executing $S.H.M.$ is

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