Example Second-Order ODE: Spring-Mass-Damper

This video solves an important second-order ordinary differential equation (ODEs): The damped harmonic oscillator for a mass on a spring with damping. We solve this by hand and also plot the solution in Python and Matlab.

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This video was produced at the University of Washington

%%% CHAPTERS %%%
0:00 Deriving the Spring-Mass-Damper Equations from F=ma
6:46 Solve the Equation by Guessing Solution x(t) = exp(a*t)
9:35 The Characteristic Equation
14:54 Using Initial Conditions to Find Undetermined Coefficients
18:08 Writing as a Matrix System of Equations
21:12 Matlab Code Example
30:44 Python Code Example

Видео Example Second-Order ODE: Spring-Mass-Damper канала Steve Brunton