Many things exhibit something that resembles simple harmonic motion (abbreviated SHO).
Waves rise and fall with a regular pattern and a slinky oscillates.
To analyze simple harmonic motion, we turn to the sine and cosine functions which are also periodic.
With a bit of tweaking, according to different amplitudes and starting points, a harmonic motion equation can describe such periodic functions.
However, such methods only work for small displacements.
When the displacements get large enough, nonlinear effects come into play.