Linear vs. Nonlinear Systems

This experiment demonstrates the superposition property for linear systems,
and the lack of superposition for nonlinear systems. This web page shows the
results of the simulation of the truck-trailer system that is described on page
10 of John Bay's book. The input is the external force applied to the
truck-trailer system, and the output is the position of the truck. The user can
enter two inputs, click on the "Run Simulation" button, and view four
graphs. The first graph is the response of the system to the first input. The
second graph is the response of the system to the second input. The third graph
is the response of the system to the *sum* of the two inputs. The fourth
graph is the sum of the first two graphs - that is, the response to the first
input plus the response to the second input. If superposition holds for the
system, then the third and fourth graphs should be identical.

Linear System

For the linear system, the spring constant K = 1, the damping constant B = 1, the trailer mass m1 = 2, and the truck mass m2 = 1.

Nonlinear System

The nonlinear system behaves the same as the linear system but with one
important difference: the spring constant K = 1.5*(x1-x2). So the spring
constant is a function of the stretching distance of the spring. This makes the
system nonlinear.

Linear Systems Experiments Home Page

Last Revised: August 5, 2002