Consider a cable loaded statically by a sinusoidal distribution of transverse load: q $=$qsin$($nx$/$L$),$ with q$=70,$ L$=25.$ The prestressing force is P $=20$qL

Same data as in Problem $1.$ Compute the approximate solution for the deflection of the wire from the Galerkin formulation. Consider a one$-$term approximation with the test function n$1=$ x $,$ and the basis function N$1=$ sin$($nx$/$L$).$

a$)$ Obtain the analytical solution of the problem.

b$)$ Compute the multiplier $1$ using Galerkin method and plot the analytical and numerical solutions. Compare analytical and numerical solutions.

c$)$ Compute the force residual rF at x$=$ L$.$

d$)$ Compute the balance residual for the approximate solution: