### Applet: The phase of an oscillator

We can represent the state of an oscillator by its *phase* $\theta(t)$, which lies in the interval $[0,2\pi]$. Since we view the phase as being a periodic variable, we can draw the interval $[0,2\pi]$ as a circle in the complex plane where $\theta$ is the angle between the positive real axis (what you might call the positive $x$-axis) and the vector from the origin to a point on the unit circle. This point is drawn in green, and you can change it by dragging it with the mouse. To display the phase most compactly, we will typically draw the phase of an oscillator as just a point on the unit circle (and omit the vector and angle shown here). The coordinates of the point in the complex plane are given by $e^{i\theta(t)}$ where $i=\sqrt{-1}$.

Applet file: oscillator_phase.ggb

#### Applet links

This applet is found in the pages

#### General information about Geogebra Web applets

This applet was created using Geogebra. In most Geogebra applets, you can move objects by dragging them with the mouse. In some, you can enter values with the keyboard. To reset the applet to its original view, click the icon in the upper right hand corner.

You can download the applet onto your own computer so you can use it outside this web page or even modify it to improve it. You simply need to download the above applet file and download the Geogebra program onto your own computer.