Consider the application relating to critical loads for a beam from Section 6.1. For

Chapter 6, Problem 9

(choose chapter or problem)

Consider the application relating to critical loads for a beam from Section 6.1. For simplicity, we will assume that the beam has length 1 and that its flexural rigidity is also 1. Following the method described in the application, if the interval [0, 1] is partitioned into n subintervals, then the problem can be translated into a matrix equation Ay = y. The critical load for the beam can be approximated by setting P = sn2, where s is the smallest eigenvalue of A. For n = 100, 200, 400, form the coefficient matrix by setting D = diag(ones(n 1, 1), 1); A = 2 eye(n) D D ; In each case, determine the smallest eigenvalue of A by setting s = min(eig(A)) and then compute the corresponding approximation to the critical load.