(35 pts) 3. Consider the fourth order differential equation describing the transverse displacement of a beam under bending with effective stiffness...

determine symmetric weak form for -u''''(x)-f(x)=0, with 4 natural boundary condition

(35 pts) 3. Consider the fourth order differential equation describing the transverse displacementof a beam under bending with effective stiffness EI=1, where E the Young‘s Modulus and I the second moment of area:—u""(:c) = f(3:), 0 < 3: <1. With this problem we need four boundary conditions, such as: u(0)=1,u'£0)=0, é- WA) lacu”(1)'=0,u”'(1‘)=-1. é- l’labwwl ha a) Determine a symmetric weak form for this problem, and state appropriateSpaces for u and test function 1:.