Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?

Options

A. a) the rotation of earth about its axis.
B. b) motion of an oscillating mercury column in a U-tube.
C. c) motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower most point.
D. d) general vibrations of a polyatomic molecule about its equilibrium position.

Explanation

(b) and (c): SHM, (a) and (d) represent periodic but not SHM [A polyatomic molecule has a number of natural frequencies, so in general, its vibration is a superposition of SHM’s of a number of different frequencies. This superposition is periodic but not SHM].