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?

In each team, students working together at a computer numbered between 1 and 10 will submit file cw5_XX_a.xlsx, students working at a computer numbered between 11 and 20 will submit file cw5_XX_b.xlsx, to the files folder in the server. Replace XX by 01 if team 1, etc. Include your name within the files.

*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:

 T