Is there a connection between the F versus x relation at the molecular level and the macroscopic relation between F and x in a spring? Explain your answer.

A simple harmonic motion is the motion in which the restoring force (F_x(x)) is proportional to displacement (x) from the mean position and opposes its increase. At molecular level the displacement is so small, that the force is always proportional to displacement. Thus in every case, it is simple harmonic motion (SHM). But at macroscopic level, the oscillations will SHM in nature only when F is linear to displacement and it is possible when displacement is very small.