Topic 13.1: Trapezoidal Rule (Engineering Application)

Contents Previous Chapter Start of Chapter Previous Topic Introduction Notes Theory HOWTO Examples Engineering Error Questions Matlab Maple Next Topic Next Chapter

Consider the differential equation

x'(t) + ax(t) = by(t)

where a and b are constants. This differential equation describes the relationship between an incoming signal x(t) and a response signal y(t). A simple system which is described by this differential equation is a resistor-capacitor (RC) circuit where the input signal is the voltage of the voltage source and the output is the voltage across the capacitor.

The coefficients a and b of the differential equation, for this application, are a = b2 = 1/RC.

This can be modeled by the following diagram, where the box with an integral

Copyright ©2005 by Douglas Wilhelm Harder. All rights reserved.