Finding the maximum value of current through the inductor

[Rick001]

Homework Statement

Homework Equations

The Attempt at a Solution

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I got the first 2 parts, but I'm having trouble with the last one. For the time the switch S₁ is closed, I derived ##q(t) = CE(1 - \cos(\frac{t}{\sqrt{LC}}))##, by writing the loop equation ##\frac{E}{L} - \frac{1}{LC}q = \frac{d^2 q}{dt^2}##, from that we get charge on the capacitor after t₀ to be CE and differentiating my expression, we get current at t=t₀ to be ##\frac{CE}{\sqrt{LC}}##, after closing S₂ and opening S₁, we have a loop where the inductor has a current ##\frac{CE}{\sqrt{LC}}## flowing through it and one capacitor has a charge CE, the other is uncharged. Now for the third part of the question, I tried finding the total energy of the components currently connected, we get a total of CE², I thought equating this to ½L(I_max)² would give me the answer, but none of them match. Why does this not work? Where is my working wrong? The answer for the last part is given as (c)

 

[TSny]

Welcome to PF!

we get a total of CE², I thought equating this to ½L(I_max)² would give me the answer, but none of them match.

You are assuming that when the current is at its maximum, all of the energy is in the inductor.

All of your other work looks correct to me.