Which one of the following statements regarding simple pendulum is correct? Simple pendulum has a time period independent of amplitude:
A.only for small amplitudes because then the net force on its bob is independent of its displacement.
B.for any amplitude because the net force on the bob is always proportional to its displacement.
C.for any amplitude because the net force on the bob is independent of its displacement.
D.only for small amplitudes because then the net force on its bob is proportional to its displacement.✓ Correct
Explanation
The restoring force on the bob of a simple pendulum is −mg sinθ. For small angles, sinθ ≈ θ (in radians), so the restoring force becomes approximately −mgθ, which is proportional to the angular displacement (i.e., simple harmonic motion). This is why the time period T = 2π√(L/g) is independent of amplitude only for small oscillations. For large amplitudes, sinθ ≠ θ and the motion is no longer simple harmonic, making the time period amplitude-dependent. Hence option (d) is correct.
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