Engineering 103 –UMass Boston

CW 5

(In-Class-Work 5)

1.- Import the data (metal distance and ultrasonic response) from http://www.itl.nist.gov/div898/handbook/pmd/section6/pmd631.htm into Excel (it helps to save them into a text file and then use ‘Data/Get External Data/Import text file’ with the ‘fixed width’ option). Produce a non-linear fit of the ultrasonic response Y’ as a function of the metal distance X, with model Y’=exp(-b1*X)/(b2+b3*X). When importing data, note that in that website, the ultrasonic response (Y) appears in the first column, and the metal distance (X) in the second column. Plot the data and best fit on a same plot. Then copy the plot into a Word file. Also provide b1, b2, b3, and the final ‘standard’ deviation coefficient.

2.- Answer the following questions about data modeling

a) Using more coefficients in a model for a given data set will lead to a lower parameter s. True or false and why?

b) In studying a phenomenon, when doing data modeling, would scientists use more or less coefficients in their models, why? What would engineers do?

c) Does the way you build your physical system affect the quality of the mathematical model you can construct? Yes or no and why?

Each student will submit Excel workbook CW5_lastname.xlsx via BlackBoard. Your full name, and date should be included within the file. If two students work together on the same file, include the second last name in each item described above. A third student will not receive credit.

*Remember that this is an individual work (turn it in, as instructed, with your name and date). Home-works and class-works count 20% toward the course grade. Class-works are done in class.

Your Excel graph should look like:

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