periodic motion
Periodic motion is any motion that repeats itself over and over in equal slices of time. Think of a child on a swing going out and back, the pendulum of an old clock ticking left and right, your own heartbeat, or the seasons returning year after year. The question it answers is simple: how do we describe something that keeps coming back to where it started and then does the very same thing again?
More precisely, a motion is periodic if, after a fixed time called the period T, the object returns to exactly the same position moving in exactly the same way, and then repeats. In symbols, x(t + T) = x(t) for every moment t, where x is the position. One full repeat is called a cycle. The number of cycles that happen each second is the frequency f, and the two are linked by f = 1 / T.
Periodic motion is one of the most common patterns in nature and the foundation for oscillations, waves, sound, light, and alternating-current electricity. One honest caution: periodic does not mean the object must travel in a straight line back and forth. A planet circling the Sun is periodic too. And not every repeating motion is the smooth, special kind called simple harmonic motion, which is only one important example.
A grandfather clock's pendulum swings once every 2 seconds. Its period T is 2 s, so its frequency is f = 1 / 2 = 0.5 cycles per second (0.5 Hz): it completes half a full swing-and-return each second.
Period and frequency are reciprocals: slow, long swings mean a big T and a small f.
Periodic just means it repeats; it does not have to be a straight back-and-forth line, and it does not have to be the smooth sinusoidal shape of simple harmonic motion.