Question $2(25$ points$)$: Consider a machine with rotating unbalance. At resonance, the maximum deflection is measured to be $0\mathrm{.}05$ m $.$ The damping ratio is estimated to be $\backslash (\backslash$zeta$=0\mathrm{.}05\backslash ).$ The out$-$ofbalance mass, $\backslash (\backslash$mathrm$\{$m$\}\_\{0\}\backslash ),$ is estimated to be $\backslash (3\backslash \%\backslash )$ of the system mass $\backslash ($ m$=110\backslash$mathrm$\{$~kg$\}\backslash ).$ Estimate the radius $\backslash ($ e $\backslash )$ of the unbalanced mass. Also determine how much mass should be added $($uniformly$)$ to the system to reduce the deflection at resonance to $0\mathrm{.}01$ m $.$