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MHT CET 2024 (16 May, Shift 2) · Energy in SHM

Energy in SHM question from MHT CET 2024 (16 May, Shift 2)

Q29MHT CET 2024 · 16 MAY · SHIFT 2Medium

Energy in SHM

The kinetic energy of a particle, executing simple harmonic motion is 16 J when it is in mean position. If amplitude of motion is 25 cm and the mass of the particle is 5.12 kg, the period of oscillation is

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Answer: (a)

KE at mean position = total energy: $\frac{1}{2}m\omega^2A^2 = 16$ J.
$\frac{1}{2}(5.12)\omega^2(0.25)^2 = 0.16\,\omega^2 = 16 \Rightarrow \omega = 10$ rad/s
$T = \frac{2\pi}{\omega} = \frac{2\pi}{10} = \frac{\pi}{5}$ s
So the answer is (a) $\frac{\pi}{5}$ s.

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