Problem $2$: For the thin disk shown in the figure, the $x=0,$ correponds to equilibrium position. The mass $m=1\mathrm{.}1kg,k=40\frac{N}{m}.$ The radius $R$ of the disk is $0\mathrm{.}15$ m $.$ The moment inertia $I_G$ about the center of mass of the thin disk as it rotates as shown in the figure is $\frac{1}{2}m{R}^2.$ Draw a freebody diagram and derive the equations of motion by Newton's method and Euler$-$Lagrange.