Task: Bilstein has developed a new shock absorber system for racing cars. This new shock has different

dampening behavior that is dependent on the amount of compression the shock is seeing. At the crossover point

$($cp$)$ of compression $(x),$ the spring constant $(k)$ changes from a linear behavior to a non$-$linear behavior. The

expressions of the spring constants at different compression ranges are shown in the table below:

Shock Behavior

The current parameters for the shock absorber are shown in the table below:

Parameters

Dampening Force $(F)$ is defined as:

$F=kx$

As the new engineer and MATLAB expert in the design group, you are tasked with writing a MATLAB code that

will plot the force as a function of compression, so the department head can visualize the dampening behavior. It

is also desired to have a warning displayed if the total travel goes past the maximum compression, which would

bottom out the shock absorber$.$ Since the spring constant, crossover point and maximum compression may still

be changed, you need to keep these as variables in your calculations for quick adjustment.

Write a MATLAB script file $(m-$ file$)$ that will calculate the dampening force $(F)$ as a function of the compression,

$($x$)$ and generates a plot.

Your script file should do the following:

A$.$ Declare all parameters as variables at the beginning of the script file and use these variables in your

subsequent calculations.

B$.$ Include detailed comments on all lines of code that say what the line of code is doing and include units, if

applicable.

C$.$ Contain a decisional structure to account for the changing spring constant with compression. The structure

should also issue a warning if the travel will exceed the maximum compression.

D$.$ Make $2$D plots of the dampening force $($F$)$ as function of compression. $($x$)$ Make a plot for two compression

ranges that are shown in the same figure window:

From $0$ to maximum compression

$2mm$ below to $2mm$ above the crossover point.

Label both axis with units, title and add grid lines on both plots.

Extra Credit $(1$pts$)$

Place the decisional structure you developed in part C in a MATLAB function file that is appended to the script

file you created. Call the function file and pass the compression, $(x)$ crossover point, $(cp)$ spring constant $)$ and

the maximum compression $(x_{-}$max$)$ to the function file to calculate the dampening force. The script and function

file must be included in $m-$file that you are submitting to CANVAS.

Criteria for Success:

To get full credit for this assignment you will have to include the following:

Include your name as the first comment in the script file.

Should not include any user input.

Detailed comments on each line of code.

Correct Decision structure to calculate the dampening force, that includes a warning branch for an exceeded

maximum compression.

Plots that are correctly labeled and including all elements called for in part D$.$

Both plots in part D are in the same figure window.

Script file $($m$-$file$)$ that correctly runs when executed on the instructor's computer.