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# Characteristics of sinusoidal oscillations

Graph of a sinusoidal oscillation

The amplitude $x_{0}$ (or $A$) of an oscillation is the magnitude of the maximum displacement (from the equilibrium point) of the physical quantity.

The amplitude of a mass oscillating vertically on a spring is the distance from its highest point to its midpoint (or its lowest point to the midpoint) of oscillation. The midpoint is the equilibrium point.

The period $(T)$ is the time taken to complete one oscillation (i.e. one complete "back-and-forth" movement).

The frequency $(f)$ is the number of oscillations completed per unit of time. The SI unit of frequency is hertz $(\text{Hz})$. The frequency is related to the period by:$$f=\frac{1}{T}$$

This means that the period and the frequency are just two different ways of expressing the same thing. The period is the time for one oscillation and the frequency is the number of oscillations per unit time.