EGM Homework 3 PDF

Preview

Summary

Third homework...

Description

Homework 3 Problems completed: 5.15, 6.1, 6.4, 6.11, S1

Problem 5.15 Figure P5.15a shows a uniform beam subject to a linearly increasing distributed load. The equation for the resulting elastic curve is (see Fig. P5.15b) Use bisection to determine the point of maximum deflection (i.e., the value of x where dy/dx = 0). Then substitute this value into Eq. (P5.15) to determine the value of the maximum deflection. Use the following parameter values in your computation: L = 600 cm, E = 50,000 kN/cm2 , I = 30,000 cm4, and w0 = 2.5 kN/cm. MATLAB Code: see file Bisection.m Output:

Problem 6.1 Employ fixed-point iteration to locate the root of f(x)= sin( x ) - x Use an initial guess of x0 = 0.5 and iterate until εa ≤ 0.01%. Verify that the process is linearly convergent as described at the end of Sec. 6.1. Solution:

Problem 6.4 Determine the lowest positive root of f(x) = 7 sin(x) e −x − 1: (a) Graphically. 2 (b) Using the Newton-Raphson method (three iterations, x0 = 0.3). (c) Using the secant method (three iterations, x-1 = 0.5 and x0 = 0.4. (d) Using the modified secant method (five iterations, x0 = 0.3, δ = 0.01). Solution:

MATLAB Code: (For the plot) see file Problem_64.m Plot:

Problem 6.11 (a) Apply the Newton-Raphson method to the function f (x) = tanh(x 2 − 9) to evaluate its known real root at x = 3. Use an initial guess of x0 = 3.2 and take a minimum of three iterations. (b) Did the method exhibit convergence onto its real root? Sketch the plot with the results for each iteration labeled. MATLAB Code: see file newtraph.m Output:

Plot:

a) Use built-in Matlab function fzero to find the root of f(x) = x^2|sinx-4=0, initial guess x0=0.5. b) Use false-position method to find the root of f(x)= x^2|sinx|-4=0, initial guess [a, b]=[0, 4]. Accept your result when |f(xi)| MATLAB Code: see files f.m, fzro.m, and falsepoint.m Output: A)

B)...