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Any motion that repeats itself identically at regular intervals. If x(t) represents the displacement of any coordinate of the system at time t, a periodic motion has the property defined by the equation below for every value of
The motion of the escapement mechanism of a watch, the motion of the Earth about the Sun, and the more complicated motion of the crankshaft, piston rods, and pistons in an engine running at uniform speed are all examples of periodic motion.
The vibration of a piano string after it is struck is a damped periodic motion, not strictly periodic according to the definition. Although the motion very nearly repeats itself, and with a fixed repetition time, each successive cycle has a slightly smaller amplitude. See Damping, Harmonic motion, Vibration, Wave motion