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For smaller angular displacement, the period of a simple pendulum depends on

  • A.its amplitude
  • B.its phase constant
  • C.its energy
  • D.the mass of the bob
  • E.its length

Answer: E

For small oscillations the period depends on its length.

For small angular displacements the motion is simple harmonic with period

\[ T = 2\pi\sqrt{\frac{l}{g}} \]

It depends only on the length l and the acceleration due to gravity g. It does not depend on the amplitude (this is the isochronism of small oscillations), on the mass of the bob, on the energy of the swing, or on the phase constant, which only fixes where in its cycle the pendulum starts.

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