A capacitor of capacitance \(C\) is charged using a battery until it reaches a potential difference \(V_0\), storing energy \(U_0\). The capacitor is then disconnected from the battery and connected in parallel with an uncharged capacitor of capacitance \(2C\) through an open switch \(S\). After switch \(S\) is closed and electrostatic equilibrium is established, what is the ratio of the total electrical energy stored in the two capacitors to the initial energy \(U_0\)?