Question

Why does an object attached to a spring undergo harmonic motion and how does its motion depend on the amplitude of oscillation?

Answer 1

A harmonic motion is a back and forth motion of an object about some mean position, which is fixed. Now, if an object is attached to a spring, and let us say we compress it by some amount and then release. What will happen, the object will start to oscillate, it is due to the spring wants its original position back, it has acquired some restoring force due to compression (or stretching). As long as there are no resistive forces (example friction, air drag or external force) the object will continue its motion.

Amplitude of oscillation is the maximum displacement of the object from the mean position. If we give more displacement, it will oscillate for larger displacements, but if we keep on increasing the amplitude (or maximum displacement), at certain limit, a point will come that the object will undergo some kind of jerky motion. Then, it will not be under harmonic motion.