$2.$ The $\backslash (10\backslash$mathrm$\{$~kg$\}/\backslash )$ mass is drop from a height of $1$ m as shown in the figure. Assume that no friction act on the rollers. Determine the mass equation of motion after the base contacts the floor. Is the system overdamped, critically damped, or underdamped? Finally, state the direction of your degree of freedom and calculate the response of the system $"\backslash ($ x$($t$)\backslash )"$ about the static equilibrium position. $(25$ points $-17$ min.$\backslash ()\backslash )$

Hint: $\backslash (\backslash$zeta$=\backslash$frac$\{$c$\}\{2\backslash$sqrt$\{\backslash$mathrm$\{$~km$\}\}\}\backslash )$