Which of the following examples represent (nearly) simple harmonic

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oscillations

#1

Which of the following examples represent (nearly) simple harmonic motion and which represent
periodic but not simple harmonic motion?
(i) The rotation of earth about its axis.
(ii) Motion of an oscillating mercury column in a U-tube.
(iii) Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower most point.
(iv) General vibrations of a polyatomic molecule about its equilibrium position.


#2

(i) There is no to and fro motion which is a must for a periodic motion to be SHM. Hence, rotation of earth about its axis is not SHM.
(it) This is a periodic motion and as it follows F = - kx (about mean position, to and fro motion) hence
SHM.
(Hi) A periodic motion, oscillatory in nature about lower most point as mean position following SHM force law hence, it is SHM,
(iv) A polyatomic molecule has a number of natural frequencies. So, in general, its vibration is a superposition of SHMs of a number of different frequencies. Thus, superposition is periodic but not necessarily SHM.