A particle executes S.H.M.,the graph of veloc | vedclass

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(C) The velocity $v$ of a particle executing $S.H.M.$ at a displacement $x$ is given by the formula: $v = \omega \sqrt{A^2 - x^2}$.Squaring both sides

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An ellipse

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(C) The velocity $v$ of a particle executing $S.H.M.$ at a displacement $x$ is given by the formula: $v = \omega \sqrt{A^2 - x^2}$.Squaring both sides,we get: $v^2 = \omega^2(A^2 - x^2)$.Rearranging the terms: $v^2 = \omega^2 A^2 - \omega^2 x^2$,which leads to $v^2 + \omega^2 x^2 = \omega^2 A^2$.Dividing both sides by $\omega^2 A^2$,we obtain: $\frac{v^2}{(\omega A)^2} + \frac{x^2}{A^2} = 1$.This equation is in the standard form of an ellipse,$\frac{y^2}{b^2} + \frac{x^2}{a^2} = 1$,where $y$ is velocity and $x$ is displacement.Therefore,the graph of velocity as a function of displacement is an ellipse.

$A$ particle executes $S.H.M.$,the graph of velocity as a function of displacement is

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