*Ordinary Differential Equations*
(ODEs) typically result
directly from Newton's laws of motion, restated here as
follows:

This is a second-order ODE relating the force on a mass at time to the second time-derivative of its position ,

If the applied force is due to a spring with spring-constant , then we may write the ODE as

(Spring Force + Mass Inertial Force = 0)

This case is diagrammed in Fig.1.2.

If the mass is sliding with *friction*, then a simple ODE model
is given by

(Spring + Friction + Inertial Forces = 0)

as depicted in Fig.1.3.

We will use such ODEs to model mass, spring, and dashpot^{2.6} elements
in Chapter 7.

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