Unit II: Second Order Constant Coefficient Linear 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:

Watch the lecture video clips:

Learn from the Mathlet materials:

Watch the problem solving video:

Complete the practice problems:

Check Yourself

Complete the problem set:

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

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Course Info

Learning Resource Types

theaters Lecture Videos
theaters Recitation Videos
grading Exams with Solutions
laptop_windows Simulations
notes Lecture Notes
assignment_turned_in Problem Sets with Solutions