Explore a comprehensive tutorial on solving second-order ordinary differential equations (ODEs) focusing on the damped harmonic oscillator for a mass on a spring with damping. Derive the spring-mass-damper equations from F=ma, solve the equation by guessing the solution x(t) = exp(a*t), and understand the characteristic equation. Learn to use initial conditions to find undetermined coefficients and write the system as a matrix. Gain practical experience with Matlab and Python code examples to plot the solution. Perfect for those studying differential equations, physics, or engineering mechanics.
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
Related Courses
-
Second-Order Ordinary Differential Equations - Solving the Harmonic Oscillator Four Ways
-
Second Order Harmonic Oscillator, Characteristic Equation, Ode45 in MATLAB
-
Modeling and Simulation of Dynamic Systems
5.0 -
A Second Course in Differential Equations
-
Higher-Order ODEs, Characteristic Equation, Matrix Systems of First Order ODEs
-
More Examples of Second Order Differential Equations
