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 answer
Explanation
The correct answer is D: the period is independent of amplitude only for small swings, because only then is the restoring force proportional to the displacement.
The restoring force on the bob is mg sin θ. For small angles sin θ is almost equal to θ, so the force becomes proportional to the displacement and points back towards the mean position. That is the condition for simple harmonic motion, and its period, T = 2π√(L/g), depends only on the length and on g, not on the amplitude or the mass. For large swings sin θ is clearly less than θ and the period grows a little.
A is wrong because the force does depend on displacement; it is its proportionality that matters.
B is wrong because the force is proportional to displacement only for small angles, not for any amplitude.
C is wrong on both counts: the result does not hold for any amplitude and the force is not independent of displacement.
Exam tip: simple pendulum is SHM only for small angles (sin θ ≈ θ); T = 2π√(L/g), independent of mass and amplitude.
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