Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations

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Taught by OCW

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Lesson Summary:

In this lesson, the focus is on analyzing second-order ODEs with complex roots, which correspond to oscillations in the solutions. The instructor addresses questions about using both roots and then moves on to discussing real solutions. The lesson ends with a method for converting complex exponential solutions to solutions with sines and cosines. This lesson is important for those interested in understanding oscillations in real-world applications.

Lesson Description:

Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations -- Lecture 10. More discussions about oscillations with second-order ODEs.

Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 26, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms

Additional Resources:

Damped Vibration Java applet - A Java applet to play around with to discover damped vibrations / oscillations.
Practice Exam 1 with Solutions - Practice Exam 1 with Solutions
Exam 1 - Exam 1
Exam 1 Solutions - Exam 1 Solutions
Lecture Notes - Lecture Notes
Muddy Card Responses - Muddy Card Responses are explanations of topics that were confusing to students
Supplementary Notes - Chapter 9 Supplementary Notes written by Prof. Miller
Recitation Problems - Recitation Problems and classwork exercises
Recitation Solutions - Recitation problem solutions
Complex Roots Java Applet - A Java Applet to use to discover complex roots visually.
Damping Ratio Java Applet - A Java applet to help you discover damping ratio and its meaning geometrically.
Damping Ratio Java Applet - A Java applet to help you discover damping ratio and its meaning geometrically.
Forced Damped Vibrations Java Applet - An interactive java applet for learning about forced damped vibrations.

Questions answered by this video:

How do you solve a damped oscillation problem?
How do you solve an undamped oscillation problem?
What are the complex roots of a second-order ODE?

Staff Review
- Currently 4.0/5 Stars.
This lesson talks more about both damped and undamped oscillation of a spring. Oscillations are associated with complex roots of a second-order ODE. A very in-depth explanation of complex solutions of ODEs.

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