The natural frequencies of vibration of a uniform beam clamped at one end and free at the other are solutions of the equation:

Investigate the roots of Equation

Matlab functions:

1. first, by graphing the equation; then

2. second, by using Newton's method.

Find the first four positive values ("physically meaningful") of the unknown.

Supply a driver script to run your functions.

Using your code and its output explain how you know your program has actually found the correct "physically meaningful" roots within the expected error tolerance.

1. Each function needs to be properly commented including a clear description of the purpose of the function, its parameter list and its return values.

For example, in Matlab this means that a user should be able use the help command to obtain information on how to use each function.

2. If multiple files are submitted a text README file which describes each of these functions should also be included.

3. All output data and plots must be properly labelled.

4. The default output for floating point numbers in Matlab is 5 digits and in Scilab it is 8. You may need to use the Sci/Matlab format command to increase the number digits output.

5. Each function should make use of vector/matrix operations where possible.

6. It is perfectly acceptable to make use of any of the built-in Sci/Matlab func-tions except the symbolic toolbox.

7. The pause command in Matlab and halt command in Scilab should be used to break up the various sections of the assignment in the main driver script and where appropriate in the functions.

9. Breakdown of marks:

• Code.
• Documentation of code.
• Formatted and Documented Results.