GRAPHING A SINE WAVE

Suppose that you draw a precise graph of the swinging object’s position with respect to time as seen from edge-on. Time is plotted horizontally; the past is toward the left, and the future is toward the right. One complete revolution of the object appears on the graph as a sine wave. Degree values can be assigned along this wave corresponding to the degrees around the circle (Fig. 1).
Constant rotational motion, such as that of the object on the string, takes place all over the universe. The child whirling the object can’t make the object abruptly slow down and speed up, or instantly stop and change direction,

Fig. 1. Graphic representation of a sine wave as circular motion.

or revolve in steps like a ratchet wheel. However, once that mass is moving, it doesn’t take much energy to keep it going. Uniform circular motion is a theoretical ideal. There’s no better way to whirl an object around and around. A sinusoid is a theoretical ideal, too. There’s no better way to make a wave.