For a damped system m$,$ c and k are known to be m $=50$ kg$,$ c $=80$ kg$/$s$,$ k$=80$ N$/$m$.$ Calculate the values of $\backslash$zeta $,$ wn$,$ fn$,$ wd and indicate the type of the damping. $($Underdamped$,$ Overdamped, Critical damped$)$

Question $1$ Select one:

$\backslash$zeta $=0\mathrm{.}452,$ wn $=3\mathrm{.}162$ rad$/$s$,$ fn $=0\mathrm{.}503$ Hz$,$ wd $=3$ rad$/$s Underdamped.

$\backslash$zeta $=0\mathrm{.}632,$ wn $=1\mathrm{.}265$ rad$/$s$,$ fn $=0\mathrm{.}201$ Hz$,$ wd $=0\mathrm{.}98$ rad$/$s Underdamped.

$\backslash$zeta $=0\mathrm{.}916,$ wn $=1$ rad$/$s$,$ fn $=0\mathrm{.}523$ Hz$,$ wd $=0\mathrm{.}98$ rad$/$s Underdamped

$\backslash$zeta $=0\mathrm{.}316,$ wn $=3\mathrm{.}282$ rad$/$s$,$ fn $=0\mathrm{.}503$ Hz$,$ wd $=9\mathrm{.}887$ rad$/$s Undamped.