help b$)$ The system shown in Figure $2$ is displaced by a distance of $3$ cm and released. A $20$ kg mass is attaching on a spring of $\backslash (400\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash )$ and dashpot of $\backslash (357\mathrm{.}8\backslash$mathrm$\{$Ns$\}/\backslash$mathrm$\{$m$\}\backslash )$ in parallel.

i$.$ Determine the natural frequency, damping ratio and state the damping condition of the system.

ii$.$ Derive the expression for the displacement from the equilibrium position in terms of time, $\backslash ($ t $\backslash )$ if the initial velocity, $\backslash (\backslash$dot$\{$x$\}=0\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Also calculate the velocity at $5$ seconds,