All undulatory phenomena are characterized by their transmission of some type of vibration. It is therefore logical to study vibrations first, especially harmonic vibrations. 

A particle which oscillates around a point of equilibrium, subject to a force proportional to the distance to this point, has a simple harmonic vibratory movement.  

A spring which is made to vibrate by a force which keeps it from equilibrium is a good example. You can study its movement in the following visual.