$3.\backslash ((30\backslash \%)\backslash )$ Consider the two member assembly shown below. The assembly is comprised of a vertical truss spring that allows for deformation along the spring axis, and a beam that allows for rotation and transverse displacement at each of its nodes. The beam and truss spring are connected via a pin joint that can slide in the global $\backslash ($ y $\backslash )$ axis. A constant distributed load $\backslash ($ T$\_\{$x$\}=$C $\backslash )$ is applied along that length of the spring, where $\backslash ($ C $\backslash )$ is a known constant with units force per length. The beam has a Young's modulus $\backslash ($ E $\backslash ),$ second moment of area $\backslash ($ I $\backslash )$ and length $\backslash ($ L$=1\backslash ).$ The spring is also of length $\backslash ($ L$=1\backslash )$ and has a stiffness $\backslash ($ k$=\backslash$frac$\{$E I$\}\{$L$^\{3\}\}=$E I $\backslash ).$ Please answer the following questions.

a$)$ List all degrees of freedom for the system, including those that are constrained

b$)$ List the degrees of freedom that are constrained $($i$.$e$.,$ boundary conditions$)$

c$)$ Assemble the global stiffness matrix $\backslash (\backslash$mathbf$\{$K$\}\backslash ).$ You do not need to include constrained degrees of freedom in this matrix!

d$)$ Assemble the global force matrix F$.$ You do not need to include constrained degrees of freedom in this matrix!

e$)$ Solve for the nodal displacements of free degrees of freedom. Your solution will be in terms of $\backslash ($ E$,$ I, C $\backslash )$