JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Elasticity & SHM

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?

Answer: (C)

Solution

For a simple harmonic oscillator of amplitude

A

and force constant

k

U = \frac{1}{2} k x^{2}, K = \frac{1}{2} k (A^{2} - x^{2})

Equating the two gives

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

, so

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

and

x = \pm \frac{A}{2}

The kinetic and potential energies are equal at the displacement

x = \pm \frac{A}{2}

JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Single correct option