Physics - SHM Question with Solution | TestHub

According to the question $$x=\mathrm{arsin}\omega t\to \frac{x}{a}=\sin \omega t$$ Now velocity $\mathrm{V}=\frac{dx}{dt}=a\omega \cos \omega t$ $\Rightarrow \frac{\mathrm{V}}{a\omega }=\cos \omega t$ From eq. (i) and (ii) $$\begin{array}{c}\frac{x^2}{a^2}+\frac{v^2}{a^2{\omega }^2}={\sin }^2\omega t+{\cos }^2\omega t\\ \frac{x^2}{a^2}+\frac{v^2}{a^2{\omega }^2}=1\end{array}$$ $\Rightarrow$ This is the equation of ellipse. So the graph between moment and displacement of particle is ellipse.