Acoustics and Vibration Animations
Daniel A. Russell
Graduate Program in Acoustics, The Pennsylvania State University

Creative Commons License CC BY NC ND This work by Dan Russell is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License . Based on a work at http://www.acs.psu.edu/drussell/demos.html . Additional information about using this content is available at http://www.acs.psu.edu/drussell/Demos/copyright.html .


The content of this page was originally posted on June 11, 2002.
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Comparing Circular and Sinusoidal Motion

animation showing uniform circular motion and the corresponding sinusoidal motion of projections to the vertical and horizontal axes.

I created the animation because I wanted to show how circular motion in the complex plane is related to the sine and cosine functions used to describe simple harmonic motion. As a point rotates counterclockwise around a circular path in the complex plane the real component (the projection onto the horizontal axes, indicated in blue) oscillates back and forth along the real (horizontal) axis as a cosine function. Meanwhile, the height of the imaginary component (red line corresponding to the projection of the circular motion onto the vertical axis) oscillates up and down as a sine function.


For a much more complete explanation of the unit circle, and how they relate to sine, cosine, and tangent functions, check out this page by my current PhD student: