Problem $2(15$ pts$)$

Given the determinate compound beam in the following $($El is constant$)$

a$.$ Plot the moment diagram directly after solving the necessary reaction forces. $(5$ pts$)($a proper coordinate system is required and must be shown to draw the shear and moment diagrams$)$

b$.$ Using the conjugate beam method to solve the rotation and the deflection at $\backslash (\backslash$mathbf$\{$C$\}\backslash )($where the force P is applied$).(10$ points$)$