Mystery Circuit in Mathematics Class

We discuss the introduction, student discovery, and teaching of a system of differential equations that model a circuit. In an engineering mathematics course we provide sufficient physics conceptual framework and differential equations background to enable students to model a given two-loop circuit and solve (using Laplace transforms and Mathematica) the system for various values of input voltage.

We give each student a unique input voltage frequency and ask for the system response to it. Students pool data, plot the results, and discover that a cascaded high-low filter circuit is the object of their study. We further enhance the modeling perspective by interpreting the system in terms of Laplace transforms and the transfer function for the system. This path permits easy computation of the gain. Students see the meaning of the transfer function and an example of the power of mathematics in analyzing technology.

Table of Contents:

ABSTRACT

INTRODUCTION

COURSE ACTIVITY
Laplace Transform Solution Strategy
Student Activity

TRANSFER FUNCTIONS IN LAPLACE TRANSFORMS

CONCLUSION

ACKNOWLEDGMENTS

REFERENCE

ABOUT THE AUTHORS