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Flash animation created with assistance from Karen Maloney, USC Advanced Instructional Media Lab.

An analogy between circular motion and sinusoidal waveform

This example was adapted from a figure in Dodge/Jerse 1997, pp. 29-30. A unit circle (radius, r = 1) is shown on the left. A corrosponding waveform--a graph of amplitude (vertical dimension) versus time (horizontal dimension)--appears at the right. On the circle, a right triangle with sides x, y and and radius r has been drawn drawn. Point P lies on the circle's perimeter at the end of r. Notice how setting P into counter-clockwise motion causes the value of x and y to vary. The length of r is, of course, constant because it is the radius of the circle. Concentrate on the variation of the length of y through time. The length of y at any given time corrosponds with the height of the waveform in the graph at the right. Dodge and Jerse refer to this as the "spoke-in-the-wheel," because it demonstrates that a relationship exists between circular motion and sinusoidal motion.