(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The first circuit has a capacitor with capacitance c and an inductor with inductance L. In series with this is another capacitor which is connected to the next loop in the circuit.

It look something like http://imgur.com/YJDaD.png"

Sorry for the crude drawing.

2. Relevant equations

The first part of the problem was to prove the equation could be written as dI^{2}/dt^{2}=w_{0}^{2}(I_{i-1}-2I_{i}+I_{i+1})

So that is a relevant equation and I have managed to do that just fine with Kirchoff's laws.

3. The attempt at a solution

The second part is to find the normal frequencies. Now I understand that this is very similar to a beaded string problem, or a discrete wave, however in the wave equation there is a Sin(k*x_{i}) and I cannot for the life of me figure out what the equivalent equation is for a circuit.

I know that the current will repeat both with the individual loops and each loop will repeat with time, but I cannot figure out how to represent the space part of the wave equation in a circuit setting. This will be necessary for me to solve the differential equation to get the normal modes...

Help?

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# Trying to calculate normal modes of nearly infinite network LC circuits

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