$5.$ A $60$ Hz generator is supplying $450$ MW $($and $0$ Mvar$)$ to an infinite bus $($with $1\mathrm{.}0$ per unit voltage$)$ through two parallel transmission lines. Each line has a per unit impedance $(100$ MVA base$)$ of $0\mathrm{.}07$j$.$ The per unit transient reactance for the generator is $0\mathrm{.}06,$ the per unit inertia constant $($H$)$ is $8$ s$,$ and damping is $10\mathrm{.}0$ per unit $($all on a $100$ MVA base$).$ At time t$=0,$ one of the tranmission lines experiences a three$-$phase short to ground at the sending end of the line, i$.$e$.,$ at the terminals of the generator. $($a$)$ Using the classical generator model, determine the pre$-$fault internal voltage magnitude and power angle of the generator. $($b$)$ Express the system dynamics during the fault as a set of first$-$order differential equations. $($c$)$ Using Euler$$s method $($even though it isn$$t numerically stable over an extended period of time$),$ determine the generator internal power angle at the end of the second time step. Use an integration step size of one cycle.