After equal intervals of time, the earth comes to the same situation, again and again, during its rotation about its axis. Hence, it is a periodic motion. However, the earth does not have a to and fro motion about its axis. So, this motion is not simple harmonic.

The mercury moves to and fro on the same path, about a fixed position, with a certain period of time. So the oscillating mercury column in a U-tube is simple harmonic.

The ball moves to and fro about the lowermost point of the bowl when released and comes back to its initial position again and again in the same period of time. Hence, its motion is periodic as well as simple harmonic.

The vibration of a polyatomic molecule is the superposition of individual simple harmonic motions of a number of different molecules. Hence, it is not simple harmonic, but periodic.