I wanted a good explanation for the difference between reciprocation and sinusoidal motion (For e.g. SHM). This question has been posted here due to many ambiguous and unclear explanations round the Web.
For a motion to be called simple harmonic, the force should be proportional and opposite to the displacement: $F = -kx$. Reciprocating motion is just a back-and-forth motion and per se, does not have to follow said law.