Here we introduce the second-order ordinary differential equation (ODEs) for a mass on a spring. In Newton's Second Law, F=ma, the acceleration a is the second derivative of the position x(t), giving a second order differential equation. We solve this equation four ways: 1) by guessing the solution, 2) using Taylor Series, 3) by guessing a different form of the solution, and 4) by writing as a matrix system of equations.

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0:00 Introduction
1:00 Deriving the Spring-Mass Equations from F=ma
6:59 Method 1: Guess the Solution!
11:57 Method 2: Taylor Series Solution
24:18 Method 3: Guess Again!
33:20 Method 4: Write as a Matrix System of Equations