Consider a simple bar fixed at one end $x=0$ and subjected to a concentrated luad of ither andive $x=180$ as shown in lie figure

$(1)$ Calculate the exact displacemant and stress destribution in the the bar.

$(2)$ Calculate the displacement and stress distribution using ritz method with the following assumption

$u=a_{1}x+a_2{x}^2$

and $,u=\frac{xu}{180},$ where $,0x180$