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.