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.