26.22: Harmonic Motion
- Page ID
- 191013
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Definitions and Theorems
Oscillatory motion is a repetitive back-and-forth or to-and-fro movement of an object around a central point or equilibrium position. This movement is characterized by a regular pattern of variation in a quantity, like displacement, velocity, or acceleration, over time.
Harmonic motion is a repetitive movement back and forth through an equilibrium point. It is characterized by a restorative force that's proportional to the displacement from equilibrium and acts in the opposite direction.
Simple harmonic motion is a special type of harmonic motion resulting from a sinusoidal oscillation which continues indefinitely. We call this type of harmonic motion a non-driven, undamped motion.
The motion of a particle undergoing simple harmonic motion is modeled using a sinusoidal function. It can be written as either\[ s(t) = A \, \sin\left( \omega t + \phi \right) \quad \text{or} \quad s(t) = A \, \cos\left( \omega t + \phi \right), \nonumber \]where the frequency of the motion is \( f = \frac{1}{\text{Period}} = \frac{\omega}{2\pi} \) cycles per unit time.