Consider a classical machine model for the generator connected to an infinite bus below. H$=5,$ D$=2,$ X$$d$=0\mathrm{.}1$ p$.$u$.,$ Zt $=$j$0\mathrm{.}1$ p$.$u$.,$ and Z$1=$Z$2=$j$0\mathrm{.}3$ p$.$u$.$ are prallel The machine is delivering $0\mathrm{.}8$ pu power at a terminal voltage of $|$Vt$|=1\mathrm{.}0782$ p$.$u$.,$ and the infinite bus has a voltage of $1$ p$.$u$.$ and derive and write out the linearized swing equation, and calculate the roots of the characteristic equations. Then, using the root to determine the oscillation parameter $($damping factor and oscillation frequency$)$ and calculate the damping ratio.