RLC Circuit Analysis with system of ODEs

[DeclanKerr]

Summary: Looking for guidance on how to model an RLC circuit with a system of ODES, where the variables are the resistor and inductor voltages.

This is a maths problem I have to complete for homework.

The problem is trying to prove that the attached circuit diagram can be modeled using the system of ODEs:

It says to do this using circuit laws, but I am having trouble working out what circuit laws to use that can allow me to create they system provided.

Any help would be appreciated.
Thanks.

 

[epenguin]

Write out all the laws that you know about capacitors, inductors, resistors, potentials and currents. What is the relation of charge and current, what is the definition of inductance? You will see that some of these laws are already in the form of differential equations. That is just to get your mind working, i.e. the fact that you do already know something and he idea of using what you already know. it's maths homework but look in your physics book, almost any fairly elementary a physics textbook covering electrical circuits. There you will find the very same problem, or very similar, explained probably better than we can do here. But before that do the first bit that I said, so that you realize that you really knew enough probably to make progress on this if you put your mind to it.

 

[rude man]

If you write the loop equation in terms of current you can substitute with the parameters in your matrix equation.
You do need the fundamental math expressions for L, R and C in terms of current and voltage as previously indicated.