JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Elasticity & SHM

A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is :

Answer: (C)

Solution

In SHM, kinetic energy

K E = \frac{1}{2} m ω^{2} (A^{2} - x^{2})

and potential energy

P E = \frac{1}{2} m ω^{2} x^{2}

. Setting

K E = P E

A^{2} - x^{2} = x^{2}

gives

A^{2} = 2 x^{2}

, so

x = \frac{A}{2}

JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Single correct option