This is an example of complex behaviour from what appears to be a simple system - a mass attached to a spring. 

A simple physics experiment involves making the mass oscillate up and down. However, under certain circumstances, when the mass used causes the rest length of the spring to extend by about one third, a curious thing happens. The vertical movement of the mass becomes unstable, and gradually the  up and down movement is replaced by a sideways motion, and the mass starts to behave like a pendulum, swinging from side to side, with no up and down motion at all. At least for a moment. Then the pendulum action starts to be replaced by the up and down movement again. The system will continue to switch between an up and down oscillation of the mass, and a sideways motion, where the mass behaves like a pendulum. 

There is a nonlinear coupling between the spring motion and the sideways pendulum motion which can become resonant for certain parameters of the system. This behaviour is known as autoparametric resonance.