Math Solution of Periodic Motion. In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of 2π radians. Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity. Any function which is not periodic is called aperiodic. Math Solution of Periodic Motion

## Math Solution of Periodic Motion

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Every day examples are seen when the variable is time; for instance, the hands of a clock or the phases of the moon show periodic behaviour. Periodic motion is motion in which the position(s) of the system are expressible as periodic functions, all with the same period.

For a function on the real numbers or on the integers, that means that the entire graph can be formed from copies of one particular portion, repeated at regular intervals.

Periodic motion of some source object is necessary to produce a sustained musical sound (i.e., one with the definite pitch and quality). For example, to produce a standard musical A (440 Hz), the source object must sustain periodic motion at 440 vibrations per second with a tolerance of less than 1 Hz -the normal human ear can detect the difference between 440 Hz and 441 Hz. The conditions necessary for periodic motion are

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