JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Elasticity & SHM

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A particle is executing Simple Harmonic Motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be:

(A) $1 : 1$
(B) $2 : 1$
(C) $1 : 4$
(D) $1 : 3$ ✓ Correct

Answer: (D)

Solution

For a particle in SHM with displacement

x = \frac{A}{2}

:

Potential energy:

P E = \frac{1}{2} k x^{2} = \frac{1}{2} k (\frac{A}{2})^{2} = \frac{1}{8} k A^{2}

Total energy:

E = \frac{1}{2} k A^{2}

Kinetic energy:

K E = E - P E = \frac{1}{2} k A^{2} - \frac{1}{8} k A^{2} = \frac{3}{8} k A^{2}

Ratio:

\frac{P E}{K E} = \frac{\frac{1}{8} k A ^{2}}{\frac{3}{8} k A ^{2}} = \frac{1}{3}

Therefore, the ratio is

1 : 3

JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Single correct option

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