Question

Which of the following examples represent (nearly) simple harmonic motion and which represent 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 polyatomic molecule about its equilibrium position.

Answer 1

(a) There is no ' to and fro ' motion which is a must for a periodic motion to be SHM . hence , rotation of earth isn't periodic motion.

(b) it is a periodic motion because it follows F = -Kx ( about .mean ans stream position ) so, it is also SHM

(c) it follows SHM law , I mean it motion of ball is opposite to direction of force .
So, it is a SHM .

(d) A polyatomic molecules has a number of natural frequencies . so, in general , its vibration is a superposition of number of different frequencies . hence it is periodic but not SHM .