Question

Which of the following examples represent (nearly) simple harmonic motion and which represents periodic but not simple harmonic motion ?
(a) the rotation of earth about its axis.
(b) motion of an oscillating mercury column in a U-tube.
(c) motion of a ball bearing inside a smooth curved bowl when released from a point slightly above the lower most point.
(d) general vibrations of a poly-atomic molecule about its equilibrium position.

Answer 1

(a) It is periodic but not Simple Harmonic Motion because it is not to and fro about a fixed point.
(b) It is a simple harmonic motion because the mercury moves to and fro on the same path, about the fixed position, with a certain period of time.
(c) It is simple harmonic motion because the ball moves to and fro about the lowermost point of the bowl when released. Also, the ball comes back to its initial position in the same period of time, again and again.
(d) A poly-atomic molecule has many natural frequencies of oscillation. Its vibration is the superposition of individual simple harmonic motions of a number of different molecules. Hence, it is not simple harmonic, but periodic.