Interpretation of the Exceptional Case: Resonance
In this lesson, students learn about resonance and how it affects differential equations. The lecture begins by reviewing the notation and facts necessary for the lesson. The professor then provides a formula for the particular solution and discusses the three possible cases. The lecture then delves into the concept of resonance by using a simple pendulum as an example. The professor uses complex equations to show how the input frequency affects the amplitude of the output. Finally, the lecture concludes by analyzing the case where the driving frequency is equal to the natural frequency, resulting in a steadily increasing amplitude.
Interpretation of the Exceptional Case: Resonance -- Lecture 14. Learn about resonance and how it impacts differential equations.
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
- Lecture Notes - Lecture Notes
- Supplementary Notes - Chapter 11 Supplementary Notes written by Prof. Miller
- Problem Set 3 - Problem Set 3
- Problem Set 3 Solutions - Problem Set 3 Solutions
- Recitation Problems - Recitation Problems and classwork exercises
- Recitation Solutions - Recitation problem solutions
- What is resonance in differential equations?
- What is a linear operator?
- What is pseduofrequency?
- What is natural damped frequency?
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Staff Review
This video lecture covers resonance and the implications of it on differential equations. Pure oscillations as well as damped resonance and their equations are discussed and solved in general form. Most all of the equations involved use sin and cos.
