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.
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