When a particle executes SHM, the nature of graphical...

For a particle executing SHM,

$x = Asin\left(\omegat + ϕ\right)$

$v = \omega Acos\left(\omegat + ϕ\right)$

$⇒ \dfrac{{v}^{2}}{{\omega}^{2}{A}^{2}} + \dfrac{{x}^{2}}{{A}^{2}} = 1 ⇒$ equation of ellipse between $v$ and $x$