Motion that repeats itself is periodic motion. A particular kind of periodic motion is known as simple harmonic motion. A particular and useful kind of periodic motion is simple harmonic motion (SHM). Our prototype for SHM is a mass attached to a spring.

The amplitude is the maximum distance the mass moves from its equilibrium position. It moves as far on one side as it does on the other.

The time that it takes to make one complete repetition or cycle is called the period of the motion. We will usually measure the period in seconds.

Frequency is the number of cycles per second that an oscillator goes through. Frequency is measured in "hertz" which means cycles per second.

Period and frequency are closely connected; they contain the same information.

T = 1/f

f = 1/T

An interesting and important characteristic of all simple harmonic motion is that the period remains the same even for motions with quite different amplitudes.

In any simple harmonic oscillator, energy continually changes from one form to another -- typically from kinetic energy to potential energy -- and back again.

For a mass-and-spring simple harmonic oscillator, the period is given by

The period of a simple pendulum is given by

Even a small force, applied at the natural frequency of an oscillating system, can cause that system to oscillate with a very large amplitude. This is known as resonance.

Damped / Driven Oscillations


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(C) 2003, Doug Davis; all rights reserved