Nonlinear systems could exhibit complicated behaviour. This is an interesting fact to be considered in different educational contexts. Our paper presents a repertory of nonlinear systems we selected to demonstrate oscillations and complex dynamics. We specify equations and values, so personal computers could be applied to solve the differential equations and to display graphically the solutions as appealing trajectories on the phase plane. The paper includes an appendix with some C code, as a programming template, and a set of references for more details. This material may be useful to teach nonlinear dynamics with the help of computers.