If displacement can be described as \(x=5 \cos (\omega t) \mathrm{mm}\), where \(\omega=6 \pi \mathrm{rad} / \mathrm{s}\), complete the following.

(a) Plot the displacement over the time interval from \(t=0\) to \(3 \mathrm{~s}\) in steps of \(0.02 \mathrm{~s}\). What is the period (in seconds) of the harmonic displacement?

(b) Plot the velocity (in \(\mathrm{mm} / \mathrm{s}\) ) over the same time interval.

(c) Plot the acceleration (in \(\mathrm{mm} / \mathrm{s}^{2}\) ) over the same time interval.

(d) Calculate the maximum velocity (i.e., calculate the time derivatives and find the maximum values) and acceleration and verify your results using your plots.