Physics - SHM Question with Solution | TestHub

The displacement equation of a particle is given by 

$$\begin{gathered} x=A\sin \left(\omega t+\varphi \right) \\ \Rightarrow \sin \left(\omega t+\varphi \right)=\frac{x}{A} \end{gathered}$$

The velocity equation is given by,

$$\begin{gathered} v=\omega A\cos \left(\omega t+\varphi \right) \\ \Rightarrow \cos \left(\omega t+\varphi \right)=\frac{v}{\omega A} \end{gathered}$$

Since, ${\sin }^2\theta +{\cos }^2\theta =1$

$\Rightarrow \frac{x^2}{A^2}+\frac{v^2}{{\omega }^2{A}^2}=1$

The above equation represents an ellipse.