$\backslash ($ A $\backslash )$ bar $\backslash ($ B C $\backslash )$ is pinned at end $\backslash ($ B $\backslash ),$ and is axially loaded by a uniform force per length $\backslash ($ f $\backslash )$ acting from $\backslash ($ x$=$L $/3\backslash )$ to $\backslash ($ x$=2$ L $/3\backslash ),$ where the origin of the $\backslash ($ x $\backslash )-$axis is at pin $\backslash ($ B $\backslash ),$ as shown. The bar has cross sectional area A and Young's modulus E$.$ Using a finite element model consisting of three elements, with each element having $2$ nodes and a length of $\backslash ($ L $/3\backslash ),$ follow the steps of finite element analysis by hand $($including displacement functions, strains, stresses, and equilibrium, as illustrated in class$)$ to estimate the axial displacements at $\backslash ($ x$=\backslash$mathrm$\{$L$\}/3\backslash ),\backslash ($ x$=2$ L $/3\backslash ),$ and $\backslash ($ x$=$L $\backslash ).$ Write your final answers in terms of $\backslash ($ f$,$ L$,$ E $\backslash ),$ and $\backslash ($ A $\backslash ).$ As part of your solution, write the final system of equations for the nodal displacements in matrix form. Weight of the bar does not come into this problem.