JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Elasticity & SHM

When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be :

Answer: (B)

Solution

For SHM, velocity is related to displacement by

v = ω A^{2} - x^{2}

.

Squaring:

v^{2} = ω^{2} (A^{2} - x^{2})

Rearranging:

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

This is the equation of an ellipse in the v-x plane.

JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Single correct option