$1.$ A $2\mathrm{.}00$ kg block is released from rest $4\mathrm{.}00$ m on a rough incline, to a massless spring with a force constant of $\backslash (\backslash$mathrm$\{$k$\}=150\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash )$ that is fixed along the rough plane as shown. If the block compresses the spring to the maximum and the coefficient of kinetic friction between the surface and the block is $\backslash (\backslash$mu$\_\{$k$\}=0\mathrm{.}15\backslash ).$

a$.$ Find how much the spring is fully compressed. $[6]$

b$.$ Find the total work done by the system. $[2]$