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Second-Order ODE: Spring-Mass-Damper

Steve Brunton via YouTube

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This course derives and solves the second-order linear ODE for a damped spring–mass system using exponential solutions, characteristic roots, and initial conditions. It also demonstrates matrix formulations and solution plots in Python and MATLAB.

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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