Spectral analysis of nonlinear systems

Two separate nonlinear differential systems are investigated in the frequency and time domains using plots generated by Mathematica. Spectral density plots are of particular interest as they can conveniently demonstrate the effect on a system of changing one of the parameters. The effects of the starting displacement on the nonlinear pendulum, and the behavior of the Lorenz system when the Rayleigh number is varied, are considered in this way.