Very few oscillations are linear, perhaps none, but many are close enough to linear, for certain restricted settings, that the popularity of linear models for real physical systems has soared.
Linear oscillators tend to be pretty dull though.
Non-linear oscillators provide a much more realistic model, and their behavior can be surprisingly complex in many cases. Non-linear oscillators will either require two differential equations, or a second order differential equation. The oscillators that will be studied in this section will all exhibit stable cycles, but note that this is not always the case, as will be seen in later sections.