RC Time Domain Response to Sinusoidal Input

This video derives the time domain response, of an RC low pass filter circuit, to a sinusoidal steady state input signal described by cosine-omega-t. The video opens with some context description and then provides a short outline of the derivation process before showing every detailed step of the derivation process. The differential equation solution approach is the method of undetermined coefficients. This video connects time domain response circuit theory with phasor domain frequency response; one can solve the circuit in either or both domains and get the same response. For more about this relation to phasor domain, please see the video: Phasors Overview – Sinusoidal Steady-State Circuit Analysis    • Phasors Overview – Sinusoidal Steady-State...   For more technical background on RC circuits, including both intuition analyses and detailed derivations of RC and RL natural and step responses, please see this book: “First and Second Order Circuits and Equations – Technical Background and Insights, which is available from John Wiley & Sons ISBN: 978-1-119-91353-5 https://www.wiley.com/en-us/First+and... 00:00 Introduction 00:13 SSS Time Domain Intro 00:58 Outline of Derivation Steps 03:24 Phasors video reference & context 03:47 Time Comain Soution Flowchart 04:11 Detailed Derivation Steps Start 04:16 Kirchhoff's Voltage Law 06:13 Method of Undeterminded Coefficients 06:51 Differentiate Proposed Solution Form 07:54 Equation 16 Holds for All Times t 08:38 1st Simultaneous Equation t=0 09:18 2nd Simultaneous Equation 10:25 Start Simultaneous Equation Solution 12:55 Coefficient A Solution 13:04 Solution for A Completed 14:09 Coefficient B Solution 14:18 Sustitute A and B into i(t) Equation 9 14:48 Express i(t) in M, Cosine, and Phi 15:07 Trig Identity cosine of sum of angles 16:43 A=McosPhi and B=-MsinPhi 18:53 Solution for Phi Completed 19:07 Derive M 19:17 Pythagorean Theorem 19:43 Unit Circle Radius Equals 1 22:25 Solution for M Completed 22:48 i(t) Solution Completed 23:06 i(t) solution matches flowchart solution