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ME EN 363-Elementary Instrumentation Lab Challenge 3: Measuring Force with Strain Gauges Goals: 1) Determine the dynamic force of a falling object Challenge: Using a bread board, configure your beam’s strain gauges in a Wheatstone bridge configuration. Also, create a LabVIEW VI that accepts a voltage input. Calibrate your Wheatstone bridge using the provided weights. Measure the dynamic force of a falling weight. Import your data into Matlab and do a Fourier analysis to determine the natural frequency of your beam from your collected data. Anchor a weight to the end of your beam and apply an impulse again. Record this data and import it into Matlab as well. Note how the natural frequency changes. Write-up: The write-up will be a full report completed by each group (One report per group) and will follow the format of the formal report described in the BYU Undergraduate Guide. The report will be due during your group’s next lab time. Refer to the report grading rubric for grading requirements. Labview Help: You’ll want to set up your Labview VI similar to your thermometer lab, with a DAQ, chart (or graph) and a Wrist to Measurement File module. You’ll also want to add a multiplier and adder in the data stream so that your program can output calibrated data. These can be found under the numeric toolbox. A sample VI is provided in the figure to the right for your convenience and to show these functions. You may want to put your program in a loop via continuous sampling. Check the sampling frequency to make sure it is adequate, but not too high. Matlab Help: First create a new m-file by clicking on the blank document in the upper left of the Matlab screen. To load your data into Matlab use either the load or importdata commands. The syntax here is (variable_name)=importdata(‘file_name’) or load(‘file_name’) (for load the variable name is the same as the file name). For syntax help in general you can simply type “help command_name” in the Matlab consol. To successfully load your data you’ll also want to make sure your working directory in Matlab is the same as the file location where your data is stored. The data in your data files is arraigned in two columns: a time column and a values column. To use this data effectively you’ll need to break it up. Extract a column of data in Matlab by typing array=matrix(:,n) where n is the column number. Use this command to extract the time and data columns as separate variables. In performing the Fourier transform we’ll need to know how many data points we have. This can be found using the length() command. You’ll also need to know the frequency the data was sampled at. This can be found by subtracting the value of the second data point from the first in the time array to find the size of the sampling increments. The frequency is the inverse of this number. Values of an array can be accessed with parenthesis. For example, in the array numbers=[5 4 7 3] in Matlab, numbers(3)=7. In a discrete Fourier transform (which is what you’re doing) the x-axis values start at zero and increment by (sampling frequency)/N, where N is the number of data points. Calculate the increment size along the x-axis and store it as a variable. To generate an array of values to be your x-axis use the syntax array=(starting values):(increment):(ending value). For example, x=0:0.5:2 would generate the array x=[0 0.5 1 1.5 2]. To perform the Fourier transform use Matlab’s fft function. It saves a lot of hassle. The syntax is transform=fft(data). The variable transform is returned as an array of complex number the length of the data set. We’ll need to adjust the amplitude of the Fourier transform or our answer will be off by a large magnitude. To do this multiply your array for the constant 2/N, where N is the number of data points in your sample. To find the magnitude of the complex number in Matlab we can use the abs(number) command, which returns the absolute value of number, but also returns the magnitude of a complex number. In Matlab number can also be an array. Create a new array comprised of the magnitudes of the Fourier transform. Finally, go ahead and plot your Fourier transform of the data. When creating more than one figure in Matlab you’ll want to declare each one. Do so by typing figure(figure number) into the line of code before your plot command. After this type stem(xvalues, yvalues) in the next line to create a stem plot. The plot() and stem() commands share the same syntax, but stem plots represent a Fourier transform more accurately. If you haven’t already, run your code to make sure it works. You’ll notice that your Fourier transform produces a graph symmetric about the y-axis. This is due to a phenomenon called aliasing. To fix this go back in to your code and adjust it to plot only half the data. The easiest way to do this is by simply restricting which data gets plotted. This is done by restricting the lengths of xvalues and yvalues. For example, xvalues(1:n) will return only up to the nth data point of xvalues. Add these restrictions to your plot and try again. Graphs can also be modified by clicking on the white mouse button above the figure on the toolbar, then double clicking on the graph. Options will appear around the graph to adjust the range and display.