Problem $1$

An LC circuit, not connected to an AC supply, cycles the energy back and forth between the inductor and the capacitor indefinitely if there is no resistance. Imagine such a circuit stores $1[$J$]$ of energy.

Part of this energy is in the inductor and another part is in the capacitor. When the current through the inductor is $\backslash (10[\backslash$mathrm$\{$~A$\}]\backslash )$ and the capacitor charge is $\backslash (5[\backslash$mathrm$\{$mC$\}]\backslash )$ the energy is split evenly.

a$)$ At this moment, what is the capacitance?

b$)$ The inductance?

c$)$ What is the natural frequency $[$cycles$/$s$]$ of this LC circuit?