Second-Order Ordinary Differential Equations - Solving the Harmonic Oscillator Four Ways
Steve Brunton via YouTube
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Overview
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This course introduces second-order ordinary differential equations through the spring-mass harmonic oscillator. It derives the model from Newton’s second law and solves it using four approaches: guessed solutions, Taylor series, an alternative solution form, and a matrix system.
Syllabus
Introduction
Deriving the Spring-Mass Equations from F=ma
Method 1: Guess the Solution!
Method 2: Taylor Series Solution
Method 3: Guess Again!
Method 4: Write as a Matrix System of Equations
Taught by
Steve Brunton