Periodic Motion

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Periodic Motion

INTRODUCTION

The vibration of a quartz crystal in a watch, the swinging pendulum of a grandfather clock, the sound vibrations produced by a clarinet or an organ pipe, the back-and-forth motion of the pistons in a car engine-all  these are examples of motion that repeats itself over and over. We call this periodic motion or oscillation, and it is the subject of this chapter. Understanding periodic motion will be essential for our later study of waves, sound, alternating electric currents, and light. A body that undergoes periodic motion always has a stable equilibrium position. When it is moved away from this position and released, a force comes into play to pull it back toward equilibrium. But by the time it gets there, it has picked up some kinetic energy, so it overshoots, stopping somewhere on the other side, and is again pulled back toward equilibrium. Picture a ball rolling back and forth in a round bowl or a pendulum that swings back and forth past its straight-down position. In this chapter we will concentrate on two simple examples of systems that can undergo periodic motions: spring-mass systems and pendulums. We will also study why oscillations often tend to die out with time and why some oscillations can build up to greater and greater displacements from equilibrium when periodically varying forces act.

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