JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Elasticity & SHM

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

Answer: (D)

Solution

For

x = A sin ω t

the velocity is

v = A ω cos ω t

. Eliminating the time with

sin^{2} ω t + cos^{2} ω t = 1

\frac{x ^{2}}{A ^{2}} + \frac{v ^{2}}{A ^{2} ω ^{2}} = 1

This is the equation of an ellipse centred at the origin, reaching

A

on the displacement axis and

A ω

on the velocity axis. The graph of velocity as a function of displacement is elliptical.

JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Single correct option