Source free series circuit

In this post, the Python modules SymPy and SciPy are used to solve for currents and voltages in a series connected circuit with a resistor, inductor and capacitor. The characteristic differential equation for the circuit is derived and solutions are obtained with SymPy and SciPy. 

A source free series RLC circuit consists of a resistor, capacitor and inductor connected in series with some initial energy stored either in the inductor, capacitor or both. Since the circuit is a single loop, the current flowing around the loop is the same current in each component. Both parallel and series connected circuits are usually presented in electrical circuit analysis classes. The two textbooks I used while in college presented the parallel connected circuit in some detail then kind of glossed over the series connect circuit since it is the dual of the other. 

The schematic for the series connected circuit is shown below.

A Jupyter notebook with the python code was used to document the analysis. To view the notebook, click here to open the notebook nbviewer (nbviewer does not execute notebooks, it only renders the inputs and outputs).

The notebook source is located on github, click here to follow the link to the repository.