Consider the beam shown below subjected to a uniformly distributed load assume w$.$ The boundary condition at $C$ is pinned and B is roller. Neglect shear and axial deformation and assume that $E$ and I are constant.

$($a$)$ Determine the slope and displacement at the end $A$ of the beam using double integration method.

$($b$)$ Determine the slope and displacement at the end $A$ of the beam using principles of virtual work.

$($c$)$ Draw free$-$body diagrams, shear, bending moment and deflection diagrams for this beam. Be sure to label values $($maximum$,$ minimum, locations, etc.$).$