The nonlinear pendulum

Abstract

1. Abstract This experiment was performed to examine the effects that linearizing equations has on the accuracy of results and to find ways of accurately determining the outcome of equations without linearization, specifically in the case of the nonlinear pendulum. It was found that for a simple pendulum, linearized equations were accurate for small values of θ and for damped oscillators, linearized equations were accurate after long time periods. It was also shown that certain characteristics of a system can be lost with linearization. The chaotic nature of a damped, driven pendulum was also probed, with graphs drawn of the phase space of the oscillator as a control parameter was incremented.