Problem $2(4$ points$)$

A $1$D bar of length $L=2$ units, area of crosssection $A=1$ unit, a uniform Young's modulus $C=10$ units, has specified displacements at its ends: $u(0)=0$ and $u(2)=0\mathrm{.}1$ as shown. There are no body forces or tractions applied to the bar.

a$)$ Write the MWR and PVW weak forms and the corresponding problem statements

b$)$ Using the Ritz method, define an approximation for displacement $u(x)$ in the form:

$u(x)$~~$h_0(x)+a_1{h}_1(x)$

i$.$e$.$ Define appropriate $h_0(x)$ and $h_1(x)$ functions for the Ritz method

c$)$ Construct the matrix form $Ka=f$ and compute the coefficient $a_1.$

d$)$ Without necessarily obtaining the exact solution, briefly comment if this $1-$term Ritz approximation would match the exact solution to this problem. Why $/$ Why not?