This video outlines the differential equation solution process used in chapter 14 of my book “First and Second Order Circuits and Equations – Technical Background and Insights”. That same chapter 14 fills in details not in the video, including solution in terms of variables alpha and zeta. Published by John Wiley & Sons, Inc., the book “First and Second Order Circuits and Equations”, (called “1st & 2nd” for short) is available here:
https://www.wiley.com/en-us/First+and+Second+Order+Circuits+and+Equations%3A+Technical+Background+and+Insights-p-9781119913535
Second order linear differential equations, with constant coefficients, are fundamental to lumped element RLC (resistor-inductor-capacitor) circuits and their driven and undriven responses. Because the entire solution process, and the discussion of the three or four damping cases, can spread across many pages in an electrical engineering textbook, I created this video overview of the classical second order time domain differential equation solution process for RLC circuits. After Kirchhoff’s laws generate the time domain differential equations, the video solves the undriven (natural response) second order differential equations for a series RLC circuit. For electrical engineering learners, there is discussion of branch relationships at about 1:20. The mathematical solution process starts at about 2:08 in the video.
