$(3)$ The equation governing the deflection of a

beam, $w(x),$ is given by

$EI\frac{d^{4}w}{d{x}^4}=p(x)$

where $p(x)$ is the distributed force along the

beam. For a cantilever beam subjected to an

end load and an end moment as shown in

Fig. $1$ :

Find the deflection of the beam using the

Galerkin method with the assumed solution

$(w)(x)=Cf(x)=C(3x^{2}l-x^3)$

where, $f(x)$ is a trial function and $C$ is a

constant. Also indicate the advantage of the

weak formulation.