Assignment for Introduction to Computational Methods | ESM 2074, Assignments of Engineering

Download Assignment for Introduction to Computational Methods | ESM 2074 and more Assignments Engineering in PDF only on Docsity! AOE/ESM 2074 Introduction to Computational Methods due 6 September 2001 1. Read Chapters 1, 2, & 3 in the Chapman text. 2. In some applications it’s useful to approximate a given function by a sum of Sine functions. f [N ](t) ≈ N∑ n=1 an sin(nt), where the an are coefficients for the specific f being approximated. As a specific example take an = 2 (−1)(n+1) n , that is f [N ](t) = 2 [ sin t − (1/2) sin 2t + (1/3) sin 3t − (1/4) sin 4t + . . .+ (−1) (N+1)x N sinNt ] Write a Matlab script to generate values of f [N ] at 101 uniformly spaced points on the interval [0, π]. Plot f [4] and f [8] on the same graph. Use the MATLAB legend command to label the individual curves. 3. A series of identical springs, each with spring constant k, is arranged in a chain. The re- lationship between the applied forces (at the connection points) and the displacements at the same points can be expressed in a matrix equation f = Kx , where f is a column vector of applied forces and x is the corresponding column of displacements, so that f = [f1f2 . . . fN ] ′ and x = [x1x2 . . . xN ] ′ . For this problem with the springs connected serially we have K =   2k −k 0 . . . 0 −k 2k −k 0 0 ... . . . . . . . . . 0 0 . . . −k 2k −k 0 . . . 0 −k k   For the case k = 10 lbs/in, and eight springs in the chain, find the displacements for an applied load of 10 lbs applied at the free end of the chain (only). You can use the diag command to build K. You can ‘solve’ for the displacement using ‘K divides f ’. 1