- #1

slantz

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## Homework Statement

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.

## Homework 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.

## 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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