A pendulum is hung from the roof of a sufficiently high building and moves freely to and fro like a simple harmonic oscillator. The acceleration of the bob is 20 m s⁻² at a distance of 5 m from the mean position. The time period of oscillation is:
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Question

A pendulum is hung from the roof of a sufficiently high building and moves freely to and fro like a simple harmonic oscillator. The acceleration of the bob is 20 m s⁻² at a distance of 5 m from the mean position. The time period of oscillation is:

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G1 Physics · Accepted Answer

Step 1: For SHM the acceleration magnitude is |a| = ω²|x|. Step 2: Given |a| = 20 m s⁻² and |x| = 5 m, ω² = 20/5 = 4 s⁻². Step 3: Thus ω = 2 rad s⁻¹. Step 4: Time period T = 2π/ω = 2π/2 = π s. Final answer: (B) π s.