# Current on Infinite Periodic LC Circuit

Kyuubi
Homework Statement:
Show that the current on an infinite periodic LC circuit obeys the wave equation in the long wavelength limit with the speed of the wave being the speed of light.
Relevant Equations:
Equations of motion of current in an LC circuit.

(In)''=1/LC(-2In +In+1 +In -1)

Note here In means i sub n. As in the current on the nth inductor.
I wrote down the equation of motion for In(t) and I'm trying to match it with infinite spring mass system equation solution. In the spring mass system, we consider A to be the equilibrium length of the springs, and we can thus write Xn(t) = X(nA,t) and put it back into the equation of motion while taking a Taylor Expansion. This allows us to model the system as a long thin rod that's been pushed. But in the infinite periodic LC Circuit, what exactly is my A? What will help me turn my In(t) to I(nA,t)? In other words, how can I change my equation of motion