A periodic motion is one that repeats itself in successive equal intervals of time. The time required for one complete repetition of the motion is called the period. The simplest periodic motion is a particle moving back and forth between two fixed points along a straight line. To undergo such a motion, the particle must be subject to a "restoring" force that is opposite to the displacement at least part of the time.
If the net force on the particle in the above periodic motion is such that the magnitude of the force is proportional to the displacement of the particle but the direction of the force is always opposite to that of the displacement (the force is always directed toward the midpoint). Namely,
F=-kx
where k is a constant and x = 0 is the midpoint. Any object that obeys this relationship is said to obey Hooke's law, and the motion that results from this specific type of net force acting on a particle is called a Simple Harmonic Motion. The most common object that obeys Hooke's law on large length scale is a spring.
Therefore, the motion of a particle on a spring is a classical example of simple harmonic motion. The diagram below illustrates an instant in such a simple harmonic motion. The points are the endpoints of the motion, where A is called the amplitude.
The motion is periodic and can be described as that of a sine function (or equivalently a cosine function), with constant amplitude. It is characterised by its amplitude, its period and its phase.
One definition of simple harmonic motion is "motion in which the acceleration of the oscillator is proportional to, and opposite in direction to the displacement from its equilibrium position".
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