Question

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

• A. elliptical
• B. parabolic
• C. straight line
• D. circular

Answer 1

The correct option is A elliptical

We know that in $\text{SHM}$,

$V=\omega$$\sqrt{A^2-x^2}$


The nature of graphical representation of velocity as a function of displacement is elliptical.

$\text{Alternate Solution}:$

$x=\text{Asin}\omega \text{t}\Rightarrow \sin \omega$t $=$ $\frac{x}{A}$

$v$ $=$ $\text{A}\omega \cos \omega \text{t}\Rightarrow \cos \omega$t $=$ $\frac{v}{A\omega }$

Hence,

$\left(\frac{x^2}{A^2}\right)+\left(\frac{v^2}{A^2{\omega }^2}\right)=1$

which is the equation of ellipse.