Maximum kinetic energy of a particle of mass 1 kg in S.H.M. is 8 J and the time period is 4 s. Maximum potential energy during the motion is 10 J. Then (a) amplitude of oscillation is nearly 4 m (b) minimum potential energy of the particle is 4 J (c) maximum acceleration of the particle is 2π m/s 2 (d) Minimum kinetic energy of the particle is 2 J

Answer: (c). ω = 2π/T = π/2 rad/s; PE has a constant offset: PEmin = 10 - 8 = 2 J, so (b) is false. Minimum KE is 0 at the extremes, so (d) is false. 1/2mω²A² = 8 ⇒ A² = (16)/(π²/4) = (64)/(π²), A = 8/π ≈ 2.55 m, so (a) is false. amax = ω²A = (π²)/(4) × 8/π = 2π m/s ² So the answer is (c).

Maximum kinetic energy of a particle of mass 1 kg in S.H.M. is 8 J… | MHT CET 2026 (14 May, Shift 1)

Q12MHT CET 2026 · 14 MAY · SHIFT 1Medium

Energy in SHM

Maximum kinetic energy of a particle of mass $1$ kg in S.H.M. is $8$ J and the time period is $4$ s. Maximum potential energy during the motion is $10$ J. Then

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Answer: (c)

$\omega = \frac{2\pi}{T} = \frac{\pi}{2}$ rad/s; PE has a constant offset: $PE_{min} = 10 - 8 = 2$ J, so (b) is false.
Minimum KE is 0 at the extremes, so (d) is false.
$\frac{1}{2}m\omega^2A^2 = 8 \Rightarrow A^2 = \frac{16}{\pi^2/4} = \frac{64}{\pi^2}$ , $A = \frac{8}{\pi} \approx 2.55$ m, so (a) is false.
$a_{max} = \omega^2A = \frac{\pi^2}{4} \times \frac{8}{\pi} = 2\pi$ m/s $^2$
So the answer is (c).

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Energy in SHM question from MHT CET 2026 (14 May, Shift 1)

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