$4.$ Consider the beam and loading shown below.

$($a$)$ What are the kinematic boundary conditions that must be satisfied by a trial displacement function if you were to use the Rayleigh$-$Ritz Method to analyze the beam shown above? $(2$ points$)$

$($b$)$ Suggest a kinematically admissible displacement field, and show that it satisfies the kinematic boundary conditions for the beam shown above. $(6$ points$)$

$($c$)$ Use your kinematically admissible displacement function to solve for any unknown constant$($s$)$ in your function using the Rayleigh$-$Ritz Method. You can assume a constant EI$.(18$ points$)$