How to Model a DC Motor as a System of ODEs

In this video, I go over the modeling of a basic DC motor as two ordinary differential equations. Timestamps: 0:00 - Introduction 0:37 - Drawing the circuit 1:46 - Deriving electrical equation (KVL) 2:43 - Drawing the mechanical system and free-body diagram 4:42 - Deriving mechanical equation (sum of torques) 5:31 - Motor Constants (Kt and Kb) 7:21 - Putting it all together If you have any questions or want to see me make a video about something, please leave a comment below! Errata: I accidentally wrote Vin instead of V in the final electrical ODE