Problem $2$: Frequency Response. Plot the magnitude and phase plots for a mass$-$spring$-($viscous$)$ damper $($MSD$)$

for damping ratios of z $=0,0\mathrm{.}01,0\mathrm{.}10,$ and $1\mathrm{.}0.$ Matlab should be used to plot these figures. Plot all of the

magnitude curves on the same Bode magnitude diagram and similarly plot all of the phase curves on the same Bode

phase diagram. Please do the following:

$$ Use normalized frequency $($w$/$wn$)$ ranging from $0\mathrm{.}01$ to $100.$

$$ In your magnitude plot, plot log amplitude vs$.$ log normalized frequency scale

$$ In your phase plot, plot phase vs$.$ log normalized frequency scale

$$ Plot the log amplitude from $0\mathrm{.}01$ to $10$

$$ Plot the phase from $180\backslash$deg to $-180\backslash$deg

Can you draw any conclusions?

b$)$ Repeat this problem for a case of hysteretic damping. Assume that h $=2$ z using the above values for z$.$ Compare

the two frequency response charts and provide some comparisons.