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

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Comparing Circular and Sinusoidal Motion

I haven't figured out exactly what I want to write as an explanation for this animation, but here's a first draft (6/11/02).

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 (blue line) oscillates back and forth along the real axis as a cosine function. Meanwhile, the height of the imaginary component (red line) oscillates up and down as a sine function.

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