$(2)$ Consider the system of Figure $2.$ The drum rotates within a nonrotating sleeve and the total assembly has a mass equal to $\backslash (\backslash$mathbf$\{4$ k g$\}\backslash ).$ The outer assembly is held in place by a spring, as shown in Figure $3.$ Note that motion is allowed only in the $\backslash ($ x $\backslash )$ direction. The spring constant $\backslash ($ k $\backslash )$ is $\backslash (500\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ).$ The ball of clothes is $7$ kg $,$ and $\backslash (\backslash$omega$=35\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash ).$

Determine the force applied to the ground.