In rectilinear motion acceleration is constant in mean and direction, in circular motion acceleration is constant but changes in direction. Periodicity varies in mean and direction with respect to pulse speed. Acceleration depends on displacement in the case of pulsating motion. The simplest relationship between acceleration and displacement may be that the acceleration of an object is proportional to its displacement. One can be defined as follows.
What is Simple Harmonic Motion?
If the acceleration of an object is proportional to its displacement from a fixed point and is always directed towards that point, then this motion of the object is called Simple Harmonic Motion.
Some examples of simple harmonics motion are the motion of a vibrating tune, the motion of a simple oscillator at short amplitude, the motion of a spring fixed at one end and a heavy object suspended at the other end, etc.