When a particle executes SHM,the nature of th | vedclass

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(B) For a particle executing $SHM$,the displacement is given by $x = A \sin(\omega t + \phi)$.Taking the derivative with respect to time,the velocity

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elliptical

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(B) For a particle executing $SHM$,the displacement is given by $x = A \sin(\omega t + \phi)$.Taking the derivative with respect to time,the velocity is $v = \frac{dx}{dt} = \omega A \cos(\omega t + \phi)$.From the displacement equation,$\sin(\omega t + \phi) = \frac{x}{A}$.From the velocity equation,$\cos(\omega t + \phi) = \frac{v}{\omega A}$.Using the identity $\sin^2 	heta + \cos^2 	heta = 1$,we get:$(\frac{x}{A})^2 + (\frac{v}{\omega A})^2 = 1$.Rearranging this,we get $\frac{x^2}{A^2} + \frac{v^2}{(\omega A)^2} = 1$.This is the standard equation of an ellipse,$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,where $a = A$ and $b = \omega A$.

When a particle executes $SHM$,the nature of the graphical representation of velocity as a function of displacement is:

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