At the first moment when the energy is shared equally by the inductor and the capacitor, what is the charge on the capacitor?

Let t = 0 Q=Qmax I=0 Energy stored in the capacitor in a LC circuit is Umax = Qmax^2 / 2c where Qmax is the initial charge stored in a capacitor.

When energy is equally shared between a capacitor and inductor, the energy stored in the capacitor becomes U = Q^2/2c.

According to the given condition, energy is equally shared between an inductor and capacitor, the energy stored in the capacitor becomes half of the initial energy.

Therefore, U = 1/2Umax Q^2/2c = 1/2 Qmax^2/2c Q^2 = 1/2 Qmax^2 Q = Qmax / square root 2