### 2 videos in "Complex Numbers"

## Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations

Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations

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Part of video series Differential Equations Course acquired through MIT OpenCourseWare

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

More info at: http://ocw.mit.edu/terms

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

- 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
- Damped Vibration Java applet - A Java applet to play around with to discover damped vibrations / oscillations.
- 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.

- 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?

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.