Engineering 103 –UMass Boston

CW 4

(In-Class-Work 4)

 

 

(a)                           Save CW3 into a new file, then in Sheet #1 modify it to produce a linear and a cubic model for the same data set, insert snapshots of these worksheets into Table 1 in a MS Word file. Make a table like the one below for the “s” values for the linear, quadratic, and cubic models, along with the coefficients obtained for each model. Indicate which is the best model (linear, quadratic, or cubic) for our set of data, and explain why.

 

Model

Coefficients

S parameter

Linear

A=

B=

C=

D=

 

 

Quadratic

A=

B=

C=

D=

 

Cubic

A=

B=

C=

D=

 

 

Table 1: All terms in polynomial models using same data set as in CW3

 

 

(b)                           Download this data set, repeat the table above for this new data set: (i) In Sheet#2 using all terms in each polynomial model. Insert spreadsheet snapshots, polynomial coefficients, and parameter s into Table 2 in your MS Word file (ii) In Sheet #3 using only the highest order term in each polynomial model. Insert spreadsheet snapshots, polynomial coefficients, and parameter s into Table 3 in your MS Word file. Can you conclude what is the dominant relationship (linear, quadratic, or cubic) between the periods and the lengths of a pendulum?

 

Model (all terms)

Coefficients

S parameter

Linear

A=

B=

C=

D=

 

 

Quadratic

A=

B=

C=

D=

 

Cubic

A=

B=

C=

D=

 

 

Table 2: All terms in polynomials models using new data set

 

 

Model (only leading terms)

Coefficients

S parameter

Linear

A=

B=

C=

D=

 

 

Quadratic

A=

B=

C=

D=

 

Cubic

A=

B=

C=

D=

 

 

Table 3: Only highest order term in polynomial models using new data set

 

 

In each team, students working together at a computer numbered between 1 and 10 will submit file cw4_XX_a.html and folder cw4_XX_a_files,  students working at a computer numbered between 11 and 20  will submit file cw4_XX_b.html and folder cw4_XX_b_files, to the files folder in the server. Replace XX by 01 if team 1, etc. Include your names 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.