In our brief treatment, we shall indicate some of the major features of this relationship and how they might be useful.įigure 3 shows the basic relationship between uniform circular motion and simple harmonic motion. If studied in sufficient depth, simple harmonic motion produced in this manner can give considerable insight into many aspects of oscillations and waves and is very useful mathematically. So observing the projection of uniform circular motion, as in Figure 2, is often easier than observing a precise large-scale simple harmonic oscillator. ![]() Hooke’s law usually describes uniform circular motions ( ω constant) rather than systems that have large visible displacements. The shadow undergoes simple harmonic motion. A ball is attached to a uniformly rotating vertical turntable, and its shadow is projected on the floor as shown. Figure 2 shows one way of using this method. ![]() There is an easy way to produce simple harmonic motion by using uniform circular motion. The shadow of a ball rotating at constant angular velocity ω on a turntable goes back and forth in precise simple harmonic motion.
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