Alternating current: acausal circuit modeling

So I decided to try something different this month and try out some acausal modeling. This should be familiar to anyone who has worked with languages like Modelica (or its proprietary cousin Dymola), but the idea with acausal modeling is to express the relationships between components, the equations that govern those components, and then let the computer sort out the rest.

For instance, I might say a component is governed by Newton's 2nd Law, F=ma, or force equals mass times acceleration. But let's say that this component only has inputs force and mass. An acausal solver would be able to "fill in" what the acceleration should be instead of making the programmer create custom relations for each combination of inputs and outputs. This, along with connecting up components, takes a ton of work off the programmer and allows simulations to be a lot more automated.

I found some interesting ways to use this for circuit simulation, so I'll show some basic examples and perhaps some with oscillatory or maybe some neat tricks with transistors if I can get it working. See you all then!