Session Overview
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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 (00:23:21)
Learn from the Mathlet materials:
- Watch the video
Exploration of the Damped Vibrations Applet (00:06:19)
Exploration of the Damped Vibrations Applet
> Download from iTunes U (MP4 - 9MB)
> Download from Internet Archive (MP4 - 9MB)
- Work with the Damped Vibrations Applet
Watch the problem solving video:
- Damped Harmonic Oscillators (00:09:29)
Complete the practice problems:
Check Yourself
Complete the problem set:
(Note: There is no Problem Set Part I in this session).