I'm wondering if the following equation makes sense, and how to solve for $\displaystyle q(t)$.

$\displaystyle -\frac{dt^2}{LC}=\frac {d^2q}{q}$.

I found this equation when trying to solve the following problem :

http://www.physicshelpforum.com/phys...pacitance.html.

I wanted to find $\displaystyle V(t)$. I realize the solution should be sinusoidal, so something like $\displaystyle V(t)=V_{max} \sin (\omega t + \phi)$.

Regarding the problem, when the capacitor halved its energy, I've found out that $\displaystyle V(0.0021s)=\frac{V_{max}}{\sqrt 2}$. So I've found the boundary values and if I find $\displaystyle V(t)$ I'm done.

If I find $\displaystyle q(t)$, I have that $\displaystyle V(t)=\frac{q(t)}{C}$ and so I'm done.

I used Kirchhoff's law of voltage to find $\displaystyle -\frac{dt^2}{LC}=\frac {d^2q}{q}$. I might have done errors though.

Thank you for any help!