II.1 Programming in MATLAB Getting Started Graphing

function [F,NA] = tfunction(beta,theta)%% tfunction.m%% This m-file is a template for a function.%% In this template, the function tfunction finds the friction force F and the normal% force NA.% The inputs to the function are the variables beta (the angle of the bar) and theta% (the angle of the incline). These two inputs are in radians.% The outputs to the function are F and NA.% Notice the syntax for the function. The output variables are surrounded by brackets,% the input variables are surrounded by parentheses, and the name of the function is% the same as the name of the file.%% This template shows:%% - the syntax for a function%W = 100;L = 2;b = [W,0,W*L/2*cos(beta)]';A = [0,1,cos(theta);1,0,-sin(theta);0,0,L*cos(theta-beta)];ainv = inv(A);x = ainv*b;F = x(1);NA = x(2);Table 3: Template for FunctionsThe M-file tfunction.m can also be called from withinanother program. So can the M-files test1 and test2. Toillustrate this, create the M-file named test2.m and type inTable 4. This program determines the critical angle beta of thebar for which the bar remains in static equilibrium but belowwhich the bar slides (See Fig. A2 – 2). The program test2.mcalls the function tfunction.m in a loop, sweeping over a rangeof values of beta between 0 and theta. Each time the function iscalled, the program compares the value of the friction forcewith the maximum allowable level of friction, F max = µN A , tosee if it’s been exceeded. To run test2.m, go to the commandwindow, type intest2and hit enter. The command window displaysbetacritical = 26.55, which is the critical angle betain degrees, and a figure window appears showing two graphs.One graph is of the friction force F versus beta and the secondgraph is of the maximum friction force (above which the barslides) versus beta.Figure A2 – 2: A bar rests on a rough surface at oneend and on a smooth inclined surface at the other end.7