(4.15) Consider a doublely built-in beam of length L with a transverse load of magnitude P in the positive direction at x = L/2. (a) By approximately minimizing the potential energy of the system find the displacement field for the beam: use a subspace with one degree of freedom. (b) Compare your approximation to the exact answer with an accurate plot of normal- C ized non-dimensional deflection versus non- dimensional position. Make sure that you clearly label your axes, have a proper aspect ratio, legend, etc. (c) Further assess the accuracy of your approxi- mate solution by computing the relative dis- placement error at the middle of the beam (as a percentage).