Harmonic motion is the concept of an oscillating system that conserves energy and momentum. Elasticity and inertia are necessary for oscillatory motion, and friction causes loss of energy. Simple harmonic motion is used to illustrate the concept, while damped motion includes friction or external forces that slow the system down. Harmonic motion has many applications in everyday life, including music.
Harmonic motion is the concept of an oscillating or repeating system such as a pendulum, spring, or the orbit of a planet around the sun. Systems in harmonic motion conserve energy and momentum as long as the internal energy remains the same. In a real system, that is not ideal, the loss of energy occurs by friction even in infinitesimal quantities due to the collision with the molecules. In order for a system to experience oscillatory motion, there must be two main qualities: elasticity and inertia; due to 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 attached to a spring or other elastic source, such as a weight attached to a spring. The movement of the object alters the speed in a sinusoidal pattern. The elastic force providing the object’s momentum increases with distance from the center of motion; the further away the object is, the greater the spring force exerted. When the object reaches the end of its motion, the force causes it to move backwards with increasing speed towards the other end of the swinging path where the cycle repeats. Simple harmonic motion is used to illustrate the concept, but it does not account for friction.
Damped motion, by comparison, includes friction or other external forces that will slow the system down and eventually reach equilibrium, or no motion at all. The more friction there is in a system, the faster a swinging object will reach equilibrium. Overdamping allows only a few oscillation cycles before equilibrium; critical damping creates a rapid return to balance, like a shock absorber in a car; and underdamping causes the oscillation to decrease over time. A more viscous medium like water creates more friction.
Harmonic movement has many applications in everyday life. Any type of oscillating system, whether it’s the pendulum in a clock, a spring in a car’s suspension system, or the rotation of an engine’s flywheel, experiences a damped form of oscillation. For example, knowing the frictional force that causes damping allows one to calculate the driving force required to maintain a constant oscillation speed in a harmonic system. There are also music applications; knowing the length of a guitar string, for example, provides a method for calculating the speed of the swing when a driving force is given, and thus the frequency of the note played.
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