EGR 103/Spring 2017/Lab 2

Introduction

For 5/5 on a homework, show your finished graph (the one that looks like Figure 2.2 from the assignment) to one of the TAs before leaving lab.

Errors / Additions

None so far for Spring 2017!

2.1 Introduction

The main purpose of this lab is to go through the process of writing a complete program to load a data set, manipulate the values, perform some analysis, and create a graph. The following is a companion piece to the lab handout itself. The sections in this guide will match those in the handout.

2.2 Resources

You will want to have a browser open with the MATLAB:Script and MATLAB:Plotting pages available to you.

2.3 Getting Started

As with last week, you will want to use the

ssh -XY netid@login-teer.oit.duke.edu

command in MobaXterm to connect to a Teer machine. Follow the directions to connect, change into your EGR103 directory, make a new folder, change into it, get the tar file, expand it, then make a copy of your lab. Finally, start MATLAB.

2.3.1 Preview

Read and work through this section, taking notes as you go. Type in the commands at the lettered sections to see how MATLAB responds.

2.3.2 .m Files

Read and work through this section, taking notes as you go. Make sure you understand why certain lines from the script produce results on the screen and others do not.

2.4 Cantilever Beam Analysis

Read and work through this section, taking notes as you go. Note especially the process of rearranging the equation to get displacement as a function of force based on the fact that - for this experiment - the independent variable is the force.

To see the data set, go to UNIX (i.e. the MobaXterm window) and type

more Cantilever.dat

You will see an 8x2 array of data. The first column of numbers is the amount of mass in kg placed on the end of the beam - for this experiment, it ranged from 0 to about 0.8 kg (i.e. about 8 N). The second column of numbers is the displacement measured in inches, because that is what the device I used measured in. You should always take data in the original units of the device; you can convert it later.

Typically, data sets should have descriptions such as the items in the data set, units, perhaps the equipment and the person who took the measurements. For this week, however, I wanted to give you a rectangular array of data that MATLAB can easily load.

2.5 Creating the Script

Note when you open a second scripts that there are tabs in the editing window; you can choose which one to make active by clicking its tab. Be careful not to accidentally click the part of the tab that closes that tab (the X).

2.5.1 Lab Manual Syntax

For this lab, there will be several times you will simply type some items into the command window to see what they do before actually adding codes to the script. Command line only items are surrounded by a box whereas code that goes in the script has a shadowbox.

2.5.2 Comments

While you are not explicitly required to include comments in your labs -- other than the header and community standard information at the top = comments are a great way to tell yourself and your TAs what you meant to do with particular chunks of code. Also, note that a line starting with %% will set off a section in the editor window. It will have no effect on the way the program runs, just what it looks like in your editing window.

2.5.3 Initializing the Workspace

Read and work through this section, taking notes as you go; note that there are several items you will simply be typing into the command window rather than your code. The lines you will actually add from item 2. of this section are the two lines (one comment, one not) at the very end of the item 2. text. Remember - if you ever get lost on what should be in this script, the completed script is at the end of the lab handout.

2.5.4 Loading and Manipulating the Data

Read and work through this section, taking notes as you go.

2.5.5 Generating Plots

Read and work through this section, taking notes as you go. Note that the code for this is pretty far under what you've written so far; you will be filling in the blank space later, just like Taylor Swift.

For the "During the lab, the instructor will have you create several different graphs in the command window..." this semester the instructor is going to let you navigate this part on your own. go ahead and look at the following alternate plotting commands by typing them in the command window only; at the end, there will be a plot command that you paste into your document:

Plotting a matrix

plot(Cantilever)

Plots the matrix itself - the data points are plotted by columns with the y value coming from the data points and the x value coming from the row of the matrix. That is why there are two lines (two columns of data) and the domain goes from 1 to 8.

Plotting with two inputs

plot(Force, Displacement)

If MATLAB gets two arguments for the plot command, the first will be the independent (typically \(x\) coordinates and the second will be the dependent (typically \(y\) coordinates). The default case is to connect the dots with blue line segments. Note for this experiment that this plot would receive no credit - among other things, the axes are not labeled and there is no title. Perhaps worse than that, you have connected eight discrete experimental data points with lines. This is not appropriate for this experiment - instead, the data points should be plotted as individual points.

Plotting different ways

Take a look at the help file for plot in MATLAB:

help plot

and in particular the table in the middle of it. The table is also available on the Pundit page for plot at MATLAB:Plotting#The_plot_Function. The table shows that, for a particular set of independent and dependent values, you can change how MATLAB makes the plot by specifying a color, a symbol, and a line style. In the absence of a color, MATLAB will default to its built in color wheel which starts with blue in the table and works its way down - skipping white. If you give a symbol but no line style, there will be no line. If you give a line style but no symbol, no symbol will appear at each point. If you give neither, solid lines with no symbol will appear. Note that in almost all cases, the order of color, symbol, and line style does not matter - ro- will produce the same as -ro. The only case where the order matters is when it comes to specifying a dash-dot line versus trying to specify a situation where there are large dots at each point and a solid line connecting the points. Take a look at

plot(Force, Displacement, 'k-.')

versus

plot(Force, Displacement, 'k.-')

as an example

Things to avoid

Here are a few examples to avoid:

plot(Force, Displacement, 'mp')

Uses purple pentagrams. It's adorable, though perhaps not professional.

plot(Force, Displacement, 'bh')

Using symbols that have cultural or religious meanings should be avoided unless wholly appropriate to the data set.

plot(Force, Displacement, 'k+')

The problem here isn't necessarily that the + look like crosses but rather that the data point in the bottom left corner looks like it might be the origin instead of a data point. Later, you will learn to use a command that zooms out so no point is on the figure boundary. For today, just avoid using the +.

The right answer

For this lab, the right answer will be to use black ink and to use circles at the points with no connecting lines, so:

plot(Force, Displacement, 'ko')

2.5.6 Polynomials in MATLAB

Read and work through this section, taking notes as you go. Be sure you and your neighbor understand how MATLAB interprets polynomials and which commands use them.

2.5.7 Generate Predictions

Read and work through this section, taking notes as you go. This part creates a new set of data points based on your equation so that you can actually plot it. You will thus have your original eight data points in Force and Displaement. You will also have 100 linearly spaced values between the minimum and maximum force value in ForceModel and the 100 calculated estimates for the displacement, based on your best straight line, in DispModel.

2.5.8 Generating Plots (revisited)

Read and work through this section, taking notes as you go. This part adds the new line to your old graph.

CRITICALLY IMPORTANT PART - never put an ending on the filname of a print command in MATLAB. MATLAB will automagically add the correct extension (for us, typically .ps) if there is not one, but if you put one, MATLAB will save the file to exactly that name. It could be a disaster if, for example you give a filename like lab2.tex...

2.6 The Assignment

Basically, once you get this script running perfectly, you are going to replicate it three times and change it to use three different data sets. Note: these three data sets are "cooked" - that is, I produced them; they did not come from an experiment.

2.6.1 What the .m-files Should Do

Read and work through this section, taking notes as you go.

2.6.2 The Lab Report

Read and work through this section, taking notes as you go. Note that the data sets have different numbers of points so the bottoms of the data tables will not line up. Also note that you should use the original data (masses and displacements in inches) in the tables -- do not put in the forces or the displacements in meters. You are using the latter in your calculations but you are presenting the original data sets here.

2.6.3 Processing the Lab Report

Seriously - spell check!