The harmonic motion can be:
Simple harmonic motion
Complex harmonic motion
Complex harmonic motion is the combination of simple harmonic motions or can say it happens when more than one simple harmonic functions combine.
Unlike simple harmonic motion, which is regardless of the forces like air resistance, friction, etc., complex harmonic motion has these forces which dissipate the initial energy and also lessen the speed and amplitude of an oscillation until the energy of the system vanishes and become rest at its equilibrium point.