Problem $1.$Consider a cable loaded statically by a sinusoidal distribution of transverse load: $=,$ with $=70,=25.$ The prestressing force is $=20.$ The left$-$hand end is pinned, and there's no force applied at the right$-$hand end. Compute the approximate solution for the deflection of the wire from the Galerkin formulation. Consider a one$-$term approximation with the test function $1=,$ and the basis function $1=$ x$2.$ 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 at $=.$ d$)$ Compute the balance residual for the approximate solution: $=22+()$