1 Introduction

Report for course EGME 511 (Advanced Mechanical Vibration). California state university, Fullerton, CA. Van der Pol differential equation is given by

\[ x^{\prime \prime }\left ( t\right ) -c\left ( 1-x^{2}\left ( t\right ) \right ) x^{\prime }\left ( t\right ) +kx\left ( t\right ) =0 \]

In this analysis, we will consider the case only for positive \(c,k\).  The above equation will be solved numerically using Matlab’s ODE45 for different initial conditions, and the phase portrait (velocity vs. displacement) is plotted to show the limit cycle for different initial conditions.