motion which results when the acceleration is proportional to the negative of the displacement

the motion of an object with acceleration proportional to the displacement, resulting in repetitive motion.

A repeating motion about a central equilibrium point (pendulum, weighted spring).

Motion whose x-t graph is a sine wave.

periodic motion in which the restoring force is proportional to the displacement

The motion of a body that is being acted on by a force (i) whose magnitude is proportional to the displacement of the body from a fixed point, and (ii) whose direction is always towards that point.

Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. The motion is periodic, as it repeats itself at standard intervals in a specific manner - described as being sinusoidal, with constant amplitude. It is characterized by its amplitude which is always positive and depends on how motion starts initially, its period which is the time for a single oscillation, and its phase which depends on displacement as well as velocity of the moving object.