1550078481-Ordinary_Differential_Equations__Roberts_

Chapter 9

Applications of Linear Systems with

Constant Coefficients

In this chapter we present several applications which require the solution of

a linear system of first-order differential equations with constant coefficients.

9.1 Coupled Spring-Mass Systems

System 1 Suppose a mass m 1 is attached to one end of a spring with spring
constant k 1. The other end of this spring is attached to a fixed support. A
second mass m2 is attached to one end of a second spring with spring constant
k 2. The other end of the second spring is attached to the bottom of mass m 1
and the resulting system is allowed to come to rest in the equilibrium position
as shown in Figure 9 .1.

01 kl

ml

-----;1-{

k2

02

System at

Equilibrium

ml

k2

Both Springs in

Stretched Position

Figure 9.1 A Coupled Spring-Mass System

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