Chapter 7.1, Problem 6E

Interpretation Introduction

Interpretation:

To show that $\dot{\text{V}}\text{ = -}\frac{\text{I}}{\text{C}}$ and $\text{V = L}\dot{\text{I}}\text{ + f}\left(\text{I}\right)$, if ${\text{V = V}}_{\text{32}}{\text{ = -V}}_{\text{23}}$, denote the voltage drop from point $\text{3}$ to point $\text{2}$ in the circuit for van der Pol oscillator. To show that these equations are equivalent to $\frac{\text{dw}}{\text{dτ}}\text{ = - x}$, $\frac{\text{dx}}{\text{dτ}}\text{ = w - μF(x)}$, where ${\text{x = L}}^{\text{1/2}}\text{ I}$, ${\text{w = C}}^{\text{1/2}}\text{ V}$, $\text{τ = }{\left(\text{LC}\right)}^{\text{-1/2}}\text{ t}$, and $\text{F(x) = f}\left({\text{L}}^{\text{-1/2}}\text{ x}\right)$.

Concept Introduction:

Kirchhoff’s voltage law (KVL) states that the summation of the voltage around a close conducting loop in the circuit must be zero, i.e., ${\displaystyle \sum \text{V = 0}}$.