Repetitive back–and–forth movement through a central, or equilibrium, position in which the maximum displacement on one side is equal to the maximum displacement on the other.

Each complete vibration takes the same time, the period; the reciprocal of the period is the frequency of vibration. The force that causes the motion is always directed toward the equilibrium position and is directly proportional to the distance from it.

Of all the different types of oscillating systems, the simplest, mathematically speaking, is that of harmonic oscillations. The motion of such systems can be described using sine and cosine function. For a given spring with constant k, the spring always puts a force on the mass to return it to the equilibrium position. The more the spring is stretched or compressed, the harder the spring pushes to return the block to its equilibrium position.

Though the spring is the most common example of simple harmonic motion, a pendulum can be approximated by simple harmonic motion, and the torsional oscillator obeys simple harmonic motion. When the oscillating object reaches maximum displacement (when it is as far from equilibrium as it can get) it changes direction. This must mean that there is an instant in time when it is not moving and at the point of maximum displacement, its speed is zero. Then it speeds up in the opposite direction, and travels fast through the equilibrium position before starting to slow again in preparation for the next change in direction.

The displacement of a particle executing simple harmonic motion at any instant is the distance of the particle from the equilibrium position at that instant.

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