Lab 13

In this lab we will experiment with Newton's method to study the performance of the method and to exercise the use of Matlab plotting functions.

The file newtonsys.m should be in your directory.

The Problem
The amount of pressure required for a large heavy object, like a house, to sink into the UN compacted homogeneous soil that lies on top of a compacted base rock can be predicted by sinking smaller objects in the same soil and recording the amount of pressure required for a fixed depth.

The model
Assume that the base rock lies a depth D below the surface. The pressure p required to sink a circular plate of radius r a total distance d <D in the UN compacted soil can be approximated by

where , and are constants. These constants depend on the degree of consolidation of the soil and d but not on the radius r.

The report from a field study of a particular muddy lot is given in the table below for a given sinking distance of 1 ft. The radii are measured in in while the pressure is measured in .

Methodology
Set up the equations needed to solve for the above constants given the measurements.

Write the appropriate function and jacobian to use Newton's method.

Implementation
Implement them in Matlab.

Applications

• Once your Matlab code is running, solve the equations with the smallest tolerance possible. Use this as the exact answer. As in the lecture notes, use it for various tolerances and construct a matrix R with the tolerance, the actual errors, and the number of iterations. Plot these in appropriate scales, and capture them with XV. Call you figures lab13a.jpg and lab13b.jpg.
• Use the code the results that obtained to predict the minimal size of circular plate needed to sustain a pressure of 500 for a sinking depth of 1 ft in the same muddy lot. Write the prediction as a script file and named it lab13.m and the results in a file named lab13results.tex.

Posting Results to the Internet
Copy your files lab13a.jpg, lab13b.jpg, lab13.m, lab13results.tex and any other file that is required to run your script, into your public_html.

Create a file lab13report.html that includes links to lab13a.jpg, lab13b.jpg, lab13.m, lab13results.tex and any other file that is required to run your script.

Modify your cs2503.html file to include a link to lab13report.html.

Handing in
Hand in using the handin command the files: lab13a.jpg, lab13b.jpg, cs2503.html, lab13report.html, lab13.m, lab13results.tex and any other file that is required to run your script.