Example Second-Order ODE: Spring-Mass-Damper @Eigensteve

Uploaded October 2022 | Updated September 2026, 1 week ago

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.

Playlist: youtube.com/playlist?list=PLMrJAkhIeNNTYaOnVI3QpH7jgULnAmvPA
Course Website: http://faculty.washington.edu/sbrunton/me564/

@eigensteve on Twitter
eigensteve.com
databookuw.com

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

Example Second-Order ODE: Spring-Mass-Damper

Complex Analysis L13: Bromwich Integrals and the Inverse Laplace Transform

Maximum Likelihood Estimation (MLE) with Examples

Additive Property of the Moment Generating Function

Properties of Chi-Squared and Students t Distributions

Hypothesis Testing Revisited: Normal, t, and Chi-Squared Distribution Tests

Neural Network Control in Collimator 2.0 & New Educational Videos!!!

High-Order Ordinary Differential Equations with More Derivatives (from Physics)

Covariance and Correlation: Example with Gaussian Distributions

PyDMD: A Python Package for Dynamic Mode Decomposition (DMD)