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PENDULUMS AND COMPLEX NUMBERS - A Free Product!

In the study of quadratic equations, students are introduced to the concepts of imaginary and complex numbers.  A common question is:  why do we have to worry about imaginary numbers?  After all, if they're imaginary, they don't exist!  This paper (Pendulums and Complex Numbers) gives a real-world example of the use of complex numbers and shows how they relate to real quantities.  We show how a quadratic equation (and complex numbers) can be used to model the dynamics of a swinging pendulum.  Equations for both a normal and an upside-down (inverted) pendulum are developed.  We also discuss how we can use mathematics to balance an inverted pendulum (the same concept used in every rocket and missile launch in history).  Hopefully, the equations presented can provide a springboard for classroom simulation studies.  Appropriate for Grades 9 and up.

The notes are presented in Microsoft Word format.  To use the notes, download the zip file and extract the file to a desired directory.  The resulting file can be opened and read in Word.

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