JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Elasticity & SHM

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In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.

(A) $\frac{1}{2}$
(B) $\frac{3}{4}$ ✓ Correct
(C) $\frac{1}{3}$
(D) $\frac{1}{4}$

Answer: (B)

Solution

With amplitude

A

, the point midway between the mean and the extreme position is at

x = \frac{A}{2}

. The total energy is

E = \frac{1}{2} m ω^{2} A^{2}

and the potential energy there is

U = \frac{1}{2} m ω^{2} (\frac{A}{2})^{2} = \frac{1}{8} m ω^{2} A^{2} = \frac{E}{4}

The kinetic energy is the remainder,

K = E - \frac{E}{4} = \frac{3 E}{4}

. The kinetic energy is

\frac{3}{4}

of the total mechanical energy.

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Single correct option

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