Problem $4.$

Consider a cable loaded statically by a uniform distribution of transverse load

$q\frac{?}{b}=ar(q)$

with $\frac{?}{\text{b}\text{a}\text{r}}(q)=100,L=50.$ The prestressing force is $P=\frac{30}{b}ar(q)L.$

The left$-$hand end is pinned, and there's a force $F_L=60$ applied downwards at the right$-$hand

end. Compute the approximate solution for the deflection of the wire from the Galerkin

formulation. Consider a two$-$term approximation with the basis functions $N_1=x,$ and $N_2=x^2$

and the test functions ${}_1=N_1,{}_2=N_2.$