This course teaches how to solve second-order ordinary differential equations (ODEs) specifically focusing on the damped harmonic oscillator for a mass on a spring with damping. The course covers deriving the equations, guessing solutions, finding undetermined coefficients, and writing the equations as a matrix system. Students will also learn to plot solutions using Python and Matlab. The teaching method includes theoretical explanations, step-by-step problem-solving, and practical coding examples. This course is intended for individuals interested in mastering second-order ODE problem-solving techniques using Python and Matlab.
Overview
Syllabus
Deriving the Spring-Mass-Damper Equations from F=ma
Solve the Equation by Guessing Solution xt = expa*t
The Characteristic Equation
Using Initial Conditions to Find Undetermined Coefficients
Writing as a Matrix System of Equations
Matlab Code Example
Python Code Example
Taught by
Steve Brunton
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