A particle of mass $m$ oscillates along $x$-axis according to equation $x=a \sin \omega t$. The natu

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A particle of mass $m$ oscillates along $x$-axis according to equation $x=a \sin \omega t$. The nature of the graph between momentum and displacement of the particle is\

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(c) : $x=a \sin \omega t$ or $\frac{x}{a}=\sin \omega t$ Velocity, $v=\frac{d x}{d t}=a \omega \cos \omega t$ $$ \frac{v}{a \omega}=\cos \omega t 	ext { or, } \frac{p}{m a \omega}=\cos \omega t 	ag{ii} $$ Squaring and adding (i) and (ii), we get\ $\frac{x^{2}}{a^{2}}+\frac{p^{2}}{m^{2} a^{2} \omega^{2}}=\sin ^{2} \omega t+\cos ^{2} \omega t ; \frac{x^{2}}{a^{2}}+\frac{p^{2}}{m^{2} a^{2} \omega^{2}}=1$\ It is an equation of ellipse.\