The switch closes at $t=0,$ and the circuit reaches a steady state at $t=T.$ The initial charges on the two capacitors are given to be $Q_1$ and $Q_2.$ Derive the amount of energy lost during the transient with the following procedures. First, express $q_2,i_1,$ and $i_2$ in terms of $q_1$ for $0tT$ by using the charge conservation relationship. Next, find $v_1$ and $v_2$ in terms of $q_1$ to define the voltage difference. After determining the power dissipated during the transient, which is $i_2(v_1-v_2),$ integrate the power over the interval $0tT$ to find the energy lost and show the energy lost is given by $(20$pt$)$