A SDOF system with a mass m$=40$ kg$,$ stiffness $2000$ N$/$m and damping ratio $=0\mathrm{.}02$ will be subjected to a load F$($t$)$ made up of three harmonic components: $3$ F$($t$)=$ sigma from $1-3$ of F$0$j$*$cos $($wj$*$aj$).$ The three components have the following characteristics: F$01=112$N F$02=230$N F$03=23$N$.$ $1$ is equal to $5$ rad$/$s$,$ $2$ is equal to $7\mathrm{.}5$ rad$/$s$,$ $3$ is equal to $2$ rad$/$s$.$ $1$ is equal to $,$ $2$ is equal to $/6,$ $3$ is equal to $/4.$ Provide a quick estimate of the maximum displacement of the mass which the load F$($t$)$ can cause. If you were to plot F$($t$)$ and x$($t$)$ based on their digital, discrete$-$time representation, what would be a suitable time$-$step for the time$-$variable t$,$ in order to provide a good illustration of all the load and the response components involved, and why?