Does this equation makes sense? If so, how to solve it?

I'm wondering if the following equation makes sense, and how to solve for .

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I found this equation when trying to solve the following problem : http://www.physicshelpforum.com/phys...pacitance.html.

I wanted to find . I realize the solution should be sinusoidal, so something like .

Regarding the problem, when the capacitor halved its energy, I've found out that . So I've found the boundary values and if I find I'm done.

If I find , I have that and so I'm done.

I used Kirchhoff's law of voltage to find . I might have done errors though.

Thank you for any help!