Chapter 6.5, Problem 5E

Interpretation Introduction

Interpretation:

To investigate the stability of equilibrium points of the given equation ${\ddot{\text{x}}\text{ = (x-a)(x}}^2-a)$ for all values of a.

Concept Introduction:

Equilibrium points of a potential are points where $\frac{\text{-dV}}{\text{dx}}\text{ = }\ddot{\text{x}}\text{ = 0}$, either denoting stable or unstable equilibrium points.

V is given as potential function for $\ddot{\text{x}}$