$ul$

$=$

$E\frac{du}{dx}$

A prismatic bar of length $10ft$ and cross$-$sectional area of $6i{n}^2$ carries a distributed load of $5l\frac{b}{f}t$ and an end load of $3000lb$ as shown in the figure above.

$($a$)$ Apply Galerkin's method using the first two basis functions of the polynomial basis

$\{{}_1=x,{}_2=x^2,$dots,${}_n=x^n\}$

and use your solution to determine Young's modulus $E($in psi$)$ so that the bar will elongate $($i$)$ no more than $2$ inches, $($ii$)$ no more than $0\mathrm{.}5$ inches.