Homework Assignment 3 Due Date: February 18 at 12:00 pm as a CANVAS upload Directions: Each student needs to submit original work. Copy and paste the MATLAB code into a word document. Include any answers to questions and plots. Please carefully read the problem. Use the Bisection Code from lab to solve the following problem. A trunnion has to be cooled before it is shrink fitted into a steel hub. Figure 1: Trunnion to be slid through the hub after contracting. The equation that gives the temperature T, (in degrees C) to which the trunnion has to be cooled to obtain the desired contraction is given by f(T) =-0.50598x10-T +0.38292 x10-T +0.74363x10 *T, +0.88318x102 = 0) Where f(T) (in millimeters) represents the difference in size between the trunnion and the hole in the hub, and f(T) = 0 means that the two are the same size. Use the Bisection Method of finding roots of equations to find the temperature T, to which the trunnion has to be cooled. Plot the equation to find the starting guesses for the Bisection Method. Conduct five iterations to estimate the root. Find the absolute relative approximate percent error at the end of each iteration. Modify the code to generate a plot of guesses vs iterations and error vs iterations. Submit the following: 1) The commands used to generate a plot showing the initial guess (include the plot in the submission) 2) Modified Bisection Code (with comments) and commands to utilize code. 3) A plot showing the guesses versus the iterations and a plot showing the error versus the iterations 4) Completed Table 1 Iteration X X X f(xi) f(x) f(x) Table 1. Homework Assignment 3 Due Date: February 18 at 12:00 pm as a CANVAS upload Directions: Each student needs to submit original work. Copy and paste the MATLAB code into a word document. Include any answers to questions and plots. Please carefully read the problem. Use the Bisection Code from lab to solve the following problem. A trunnion has to be cooled before it is shrink fitted into a steel hub. Figure 1: Trunnion to be slid through the hub after contracting. The equation that gives the temperature T, (in degrees C) to which the trunnion has to be cooled to obtain the desired contraction is given by f(T) =-0.50598x10-T +0.38292 x10-T +0.74363x10 *T, +0.88318x102 = 0) Where f(T) (in millimeters) represents the difference in size between the trunnion and the hole in the hub, and f(T) = 0 means that the two are the same size. Use the Bisection Method of finding roots of equations to find the temperature T, to which the trunnion has to be cooled. Plot the equation to find the starting guesses for the Bisection Method. Conduct five iterations to estimate the root. Find the absolute relative approximate percent error at the end of each iteration. Modify the code to generate a plot of guesses vs iterations and error vs iterations. Submit the following: 1) The commands used to generate a plot showing the initial guess (include the plot in the submission) 2) Modified Bisection Code (with comments) and commands to utilize code. 3) A plot showing the guesses versus the iterations and a plot showing the error versus the iterations 4) Completed Table 1 Iteration X X X f(xi) f(x) f(x) Table 1
