Chapter 2.7, Problem 7E

Interpretation Introduction

Interpretation:

It is to be proved that, the solutions of $\dot{\text{x}}\text{ = f(x)}$ cannot oscillate using the existence of a potential function $\text{V(x)}$.

Concept Introduction:

V(t) is a decreasing function of time. So, the potential of a particle decreases along its path and the particle always tends to move toward lower potential.

The potential of the particle remains constant only at equilibrium.