What Is Harmonic Motion?

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  • Written By: Michael Smathers
  • Edited By: Jessica Seminara
  • Last Modified Date: 06 October 2019
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Harmonic motion is the concept of an oscillating, or repeating, system such as a pendulum, a spring or the orbit of a planet around the sun. Systems that are in harmonic motion conserve energy and momentum as long as the internal energy remains the same. In an actual system, i.e., non-ideal, energy loss occurs due to friction even in infinitesimal amounts because of collision with molecules. Two main qualities must exist for a system to experience oscillatory motion: elasticity and inertia; because of Newton's first law, all objects have inertia. Therefore, a source of elasticity must exist, such as a spring.

A simple harmonic system includes one or more oscillating objects that are fixed to a spring or other elastic source, such as a weight attached to a spring. The motion of the object alters speed in a sinusoidal pattern. The elastic force that provides the object momentum increases with the distance from the center of motion; the farther away the object is, the more elastic force is exerted. When the object comes to the end of its motion, the force causes it to move backward at increasing speed to the other end of the oscillating path where the cycle repeats. Simple harmonic motion is used to illustrate the concept, but does not take friction into account.


Dampened motion, by comparison, includes friction or other outside forces that will slow the system down and eventually cause it to reach equilibrium, or no motion. The more friction there is in a system, the quicker an oscillating object will reach equilibrium. Overdamping allows only a few cycles of oscillation before equilibrium; critical damping creates a quick return to equilibrium, such as a shock absorber in a car; and underdamping causes the oscillation to decrease over time. A more viscous medium such as water creates more friction.

Harmonic motion has many applications in day-to-day life. Any type of oscillating system — whether a clock's pendulum, a spring from a car's suspension system or the turning of an engine's flywheel — undergoes a form of dampened oscillation. For example, knowing the force of friction that causes damping allows calculation of the driving force necessary to maintain a constant rate of oscillation in a harmonic system. There are also musical applications; knowing the length of a guitar string, for instance, provides a method of calculating the rate of oscillation when given a driving force, and therefore the frequency of the note played.


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