Using MATLAB, solve the following problem:

$1.$ For the solid cylinder $[$part $($a$)$ in figure to right$]$ and loading shown, find the maximum shearing stress. Describe your solution process and keep your answer in symbolic form. Develop a MATLAB program to support a discussion describing how the maximum shearing stress is affected by a change in the applied torsion and the cylinder diameter. Feel free to use this MATLAB script shell $\backslash (\backslash$downarrow $\backslash )$ as a starting point or develop your own. Note the Matlab shell provided is for a different problem and as such $"$do not" follow its guidance. Simply use the script as an example of formatting.

$2.$ Using the result from question $1$ above for part $\backslash ($ a $\backslash ),$ determine the inner diameter of the cylinder shown, for which the maximum stress is the same as in part $\backslash ($ a $\backslash ).$ Analyze the result and suggest why you think it is right. This should include, but not limited to: are the basic dimensions correct? Assume dt is known and larger than ds$.$

$3.$ Using a new MATLAB script, show how the inner radius of the tube changes as a function to the outer diameter. For this analysis, use a diameter of $3$ inches for the solid cylinder and vary the outer tube diameter $3\mathrm{.}2$ to $5$ inches. You must select $($estimate$/$guess$)$ the proper range here in order to produce the desired plot. Finally, using the graph you just developed, estimate the inner diameter of the tube that has an outer diameter of $4$ inches.

For this discussion, upload your Program Outline to this discussion by the fourth day at $11$:$59$ pm of this module week. Address at least two other students' outlines by the sixth day at $11$:$59$ pm of this module week, and follow up on any addressed to you before the last day of this module week at $11$:$59$ pm$.$

Review the Important Information about MATLAB Discussions page for more information on the discussion expectations.