Differential Equations

Damped Harmonic Oscillators

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Session Overview

In this session we apply the characteristic equation technique to study the second order linear DE mx" + bx’+ kx’ = 0. We will use this DE to model a damped harmonic oscillator. (The oscillator we have in mind is a spring-mass-dashpot system.) We will see how the damping term, b, affects the behavior of the system. The system will be called overdamped, underdamped or critically damped depending on the value of b.

Session Activities

Read the course notes:

• Damped Harmonic Oscillators: Introduction (PDF)
• Damped Harmonic Oscillators (PDF)
• Under, Over and Critical Damping (PDF)

Watch the lecture video clips:

• Damping and Pseudo-Frequency

Learn from the Mathlet materials:

• Watch the video Exploration of the Damped Vibrations Applet
• Work with the Damped Vibrations Applet

Watch the problem solving video:

• Damped Harmonic Oscillators

Complete the practice problems:

• Practice Problems 10 (PDF)
• Practice Problems 10 Solutions (PDF)

Check Yourself

Complete the problem set:

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

(Note: There is no Problem Set Part I in this session).

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