Peridic functions are extremely important. Many circular motions are periodic, as are many sums of trigonometric functions.

Motion in a circle with constant speed can be written in Cartesian form aswhereis the radius of rotation and the amplitude of the vibration projected onto the x or y axes.

Any function of the formis also periodic. We can writewhereandifandif

If the motion of a particle is described by a functionthen the motion is periodic with amplitude A, periodand phase

Example:We can write it aswhereThe amplitude of the motion isthe period isand the phase isThe motion of the particle is shown below.