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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.