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 lowermost point.
$(d)$ General vibrations of a polyatomic molecule about its equilibrium position.

(B, C) and $(c)$ represent simple harmonic motion $(SHM)$,while $(a)$ and $(d)$ represent periodic motion that is not $SHM$.
$(a)$ The rotation of Earth about its axis is a periodic motion because it repeats its orientation at equal intervals of time. However,it is not $SHM$ because it does not involve a to-and-fro motion about a fixed equilibrium point.
$(b)$ An oscillating mercury column in a $U$-tube is $SHM$. The mercury moves to-and-fro along the same path about a fixed equilibrium position with a constant period,satisfying the conditions for $SHM$.
$(c)$ When a ball bearing is released from a point slightly above the lowermost point of a smooth curved bowl,it oscillates to-and-fro about the equilibrium position. For small displacements,the restoring force is proportional to the displacement,making it $SHM$.
$(d)$ The vibrations of a polyatomic molecule are periodic but not $SHM$. $A$ polyatomic molecule has multiple natural frequencies of oscillation,and its overall vibration is a superposition of several different simple harmonic motions.