Differential Equations

ODE's with Periodic Input, Resonance

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Session Overview

We learn how to solve constant coefficient DE’s with periodic input. The method is to use the solution for a single sinusoidal input, which we developed in Unit 2, and then superposition and the Fourier series for the input. We also discuss the relationship of Fourier series to sound waves.

Session Activities

Read the course notes:

• ODE’s with Periodic Input, Resonance: Introduction (PDF)

Watch the lecture video clip:

• Solving ODE’s, Resonant Frequencies

Read the course notes:

• Examples: Simple Harmonic Oscillator (PDF)

Learn from the Mathlet materials:

• Read about how to work with the Harmonic Frequency Response Applet (PDF)
• Work with the Harmonic Frequency Response: Variable Natural Frequency Applet

Read the course notes:

• Example: Damped Harmonic Oscillator (PDF)
• General Case (PDF)

Watch the lecture video clips:

• Hearing I
• Hearing II

Learn from the Mathlet materials:

• Read about how to work with the Fourier Coefficients: Complex with Sound Applet (PDF)
• Work with the Fourier Coefficients: Complex with Sound Applet

Watch the problem solving video:

• Linear ODE’s with Periodic Input

Complete the practice problems:

• Practice Problems 23 (PDF)
• Practice Problems 23 Solutions (PDF)

Check Yourself

Complete the problem sets:

• Problem Set Part I Problems (PDF)
• Problem Set Part I Solutions (PDF)
• Problem Set Part II Problems (PDF)
• Problem Set Part II Solutions (PDF)

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