Hookian Springs

For a so$-$called Hookian spring, an applied force $F$ results in a displacement $x$ according to the equation:

$F=kx$

where $k$ is the spring constant $(\frac{N}{m}).$ Despite its name, $k$ does vary under certain circumstances; for instance, as the result of a change in temperature.

A fixed load of $17N$ was applied to a spring over a range of temperatures $T(C),$ and the resulting displacements $x$ were measured $(m).$ The data are contained in the ME$2004\_$HOokianSpringsData.mat file on Canvas.

Develop a script $.$m$-$file which:

Loads the $.$mat file

Computes $k$ for each temperature.

Plots $k$ vs$.T.$ Refer to the course FAQ on Canvas for detailed requirements defining plot formatting $($titles$,$ labels, etc.$).$

Briefly describe how the spring constant $k$ changes with temperature.

Why do you think the spring behaves this way?

$3$