An object of mass 0.2 kg executes simple harmonic oscillations along the x -axis with frequency of (25/π)Hz. At the position x = 0.04 m, the object has kinetic energy 1 J and potential energy 0.6 J. The amplitude of oscillation is (a) 0.06 m (b) 0.6 m (c) 0.08 m (d) 0.8 m

Answer: (c). ω = 2π × 25/π = 50 rad/s E = 1 + 0.6 = 1.6 J E = 1/2mω²A² = 1/2(0.2)(2500)A² = 250A² A² = (1.6)/(250) = 0.0064 ⇒ A = 0.08 m So the answer is (c) 0.08 m.

An object of mass 0.2 kg executes simple harmonic oscillations along… | MHT CET 2025 (23 Apr, Shift 2)

Q22MHT CET 2025 · 23 APR · SHIFT 2Medium

Energy in SHM

An object of mass 0.2 kg executes simple harmonic oscillations along the x -axis with frequency of $\left(\frac{25}{\pi}\right)\text{Hz}$ . At the position $x = 0.04\text{ m}$ , the object has kinetic energy 1 J and potential energy 0.6 J. The amplitude of oscillation is

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Answer: (c)

$\omega = 2\pi \times \frac{25}{\pi} = 50$ rad/s
$E = 1 + 0.6 = 1.6$ J
$E = \frac{1}{2}m\omega^2A^2 = \frac{1}{2}(0.2)(2500)A^2 = 250A^2$
$A^2 = \frac{1.6}{250} = 0.0064 \Rightarrow A = 0.08$ m
So the answer is (c) 0.08 m.

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