Chapter 7.6, Problem 11E

Interpretation Introduction

Interpretation:

To solve for ${\text{x}}_{\text{1}}$, for the van der Pol oscillator system given by $\ddot{\text{x}}\text{ + x + ε}\left({\text{x}}^{\text{2}}\text{- 1}\right)\dot{\text{x}}\text{ = 0}$, assuming that the original system had the initial conditions $\text{x}\left(\text{0}\right)\text{ = 2}$, $\dot{\text{x}}\left(\text{0}\right)\text{ = 0}$.

Concept Introduction:

The van der Pol oscillator system is given by

$\ddot{\text{x}}\text{ + x + ε}\left({\text{x}}^{\text{2}}\text{- 1}\right)\dot{\text{x}}\text{ = 0}$.

The equations for $\dot{\text{x}}$ and $\ddot{\text{x}}$ are given as:

$\dot{\text{x}}\text{ = }\frac{\text{dx}}{\text{dt}}$

$\ddot{\text{x}}\text{ = }\frac{{\text{d}}^2\text{x}}{{\text{dt}}^2}$