$($System is spring$-$block$-$earth$)$ A mass M $=3\mathrm{.}5$ kg block starts at the top of a smooth curved ramp and is released at rest as shown in the figure. It slides down the ramp and onto a horizontal floor that has a rough patch $(\backslash$mu s $=0\mathrm{.}120,\backslash$mu k $=0\mathrm{.}175)$ of length $3\mathrm{.}00$ m and then continues to hit and compress a spring before rebounding. If the spring constant of the spring is $400$ N$/$m$,$ determine the maximum distance $($m$)$ the spring is compressed. Give answer to three places to the right of the decimal.