$2.$ A spring is stretched $0\mathrm{.}62$ m from equilibrium by a force of $199$ N$.[16$C$]($a$)$ Determine the spring constant.$($b$)$ Calculate the magnitude of the force required to stretch the spring $0\mathrm{.}25$ m from equilibrium.$($c$)$ Determine the work done on the spring to stretch it $0\mathrm{.}25$ m from equilibrium.$($d$)$ Determine the work done on the spring to compress it $0\mathrm{.}50$ m from equilibrium.