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.
Read the course notes:
- Damped Harmonic Oscillators: Introduction (PDF)
- Damped Harmonic Oscillators (PDF)
- Under, Over and Critical Damping (PDF)
Watch the lecture video clips:
Learn from the Mathlet materials:
- Watch the video Exploration of the Damped Vibrations Applet (00:06:19)
Exploration of the Damped Vibrations Applet
- Transcript (PDF)
- Work with the Damped Vibrations Applet
Watch the problem solving video:
Complete the practice problems:
Complete the problem set:
(Note: There is no Problem Set Part I in this session).