Chapter 7.3, Problem 6E

Interpretation Introduction

Interpretation:

For the oscillator equation $\ddot{\text{x}}\text{ + F(x,}\dot{\text{x}}\text{)}\dot{\text{x}}\text{ + x = 0 }$, give physical interpretation of the assumption on $\text{F}$, where $\text{F(x,}\dot{\text{x}}\text{) < 0}$ if $\text{r }\le \text{ a }$ and $\text{F(x,}\dot{\text{x}}\text{) > 0}$ if $\text{r }\ge \text{ b}$, ${\text{r}}^2{\text{= x}}^2{\text{+}\dot{\text{x}}}^2$ Show that there is at least one closed orbit in the region $\text{a < r < b }$.

Concept Introduction:

Identify the trapping region. In the trapping region fixed point doesn’t exist. Hence, there must a closed orbit in the region $\text{a < r < b }$.