An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of the object at an instant t = T/4 s starting from mean position. Assume that the initial phase of the oscillation is zero. (a) 0.62 J (b) 6.2 × 10 - 3 J (c) 1.2 × 103 J (d) 6.2 × 103 J

Answer: (a). At t = T/4 from the mean position the particle is at the extreme, x = A, so all energy is potential. ω = 2π/T = (2π)/(0.2) = 10π rad/s U = 1/2mω²A² = 1/2(0.5)(10π)²(0.05)² ≈ 0.62 J So the answer is (a) 0.62 J.

An object of mass 0.5 kg is executing simple harmonic motion. It… | JEE Main 2021 (27 Jul, Shift 2)

Q63JEE Main 2021 · 27 JUL · SHIFT 2Medium

Energy in SHM

An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of the object at an instant $t = \frac{T}{4}\text{ s}$ starting from mean position. Assume that the initial phase of the oscillation is zero.

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Answer: (a)

At $t = \frac{T}{4}$ from the mean position the particle is at the extreme, $x = A$ , so all energy is potential.
$\omega = \frac{2\pi}{T} = \frac{2\pi}{0.2} = 10\pi$ rad/s
$U = \frac{1}{2}m\omega^2A^2 = \frac{1}{2}(0.5)(10\pi)^2(0.05)^2 \approx 0.62$ J
So the answer is (a) $0.62$ J.

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