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Oscillations

The Oscillations paradigm explores the dynamics of mechanical and electrical oscillations. We begin by studying the free, undamped motion of a real pendulum in one dimension to learn the principles of periodic motion, both harmonic and anharmonic. Study of the driven oscillator gives insight into the frequency response and resonance, and is the vehicle to introduce Fourier series. Damping is introduced, of course, to model real systems, and Fourier integrals are introduced near the end of the course as a limiting case of Fourier series. The course is centered on three laboratory activities (a physical pendulum, a driven LRC circuit, and a pulsed LRC circuit), supported by lecture/discussion and guided data analysis activities. We use complex numbers throughout the analysis so that students learn this important tool. (more...)

Textbook:

Sample Syllabus Fall 2009

Course Contents

Unit: The Period of a Pendulum (Potential energy diagrams and integrated lab)

Potential energy diagrams (50 minutes)

Pendulum lab (50 minutes)

Pendulum period calculation (110 minutes)

Unit: Representing Harmonic Motion

Real representations (30 minutes)

Complex representations (70 minutes)

The simple harmonic oscillator (50 minutes)

Unit: Damped Harmonic Motion

The underdamped oscillator (50 minutes)

Unit: Driven Harmonic Oscillator, Fourier Series & Resonance

Single-Frequency Sinusoidal Driving Force (150 minutes)

Building & deconstructing periodic functions (xx minutes)

Unit: Response to an Impulse & a Simple Fourier Integral

Response to an impulse & a simple Fourier integral (xx minutes)


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