Advanced Engineering Mathematics, 7th Edition

3.11 Nonlinear Models

INTRODUCTION

In this section we examine some nonlinear higher-order mathematical models. We are able to solve some of these models using the substitution method introduced on page 153. In some cases where the model cannot be solved, we show how a nonlinear DE can be replaced by a linear DE through a process called linearization.

Nonlinear Springs

The mathematical model in (1) of Section 3.8 has the form

(1)

where F(x) = kx. Since x denotes the displacement of the mass from its equilibrium position, F(x) = kx is Hooke’s ...