Use the Galerkin method for #1 and the Rayleigh-Ritz method for #2.

Instructions: Show your work. If you use MATLAB or another software package to help you, turn in a printout showing what you typed in, how the problem was solved, etc Problem 1: A uniform bar is fixed at both ends and subjected to a distributed axial load q(x) (see drawing below). The values defining the bar and load are: A-500 mm2, E-100 MPa, L-0.6m, c 200 kN/m (watch your units!). Using the Galerkin method with an assumed quadratic polynomial solution, determine the axial force distribution P(x) along the bar. Plot P(x) for OSxS L. Find the reaction forces at the left and right sides and the total force due to q(x), and sum them to determine whether static equilibrium is satisfied. If equilibrium is not satisfied, what does that tell you about yor assumed solution? Problem 2 Solve for the force distribution P(x) in Problem 1 using the Rayleigh-Ritz method (the principle of minimum potential energy)