Problem $2.$ A disk of mass $m=10kg$ is rolling

without slipping on an incline of angle $=30$ in

vertical plane. The center of the disk is attached to two

springs of stiffness $k_1=500\frac{N}{m}$ and $k_2=1000$

$\frac{N}{m},$ and its position $x$ is measured from where both

springs are unstretched. Use $g=9\mathrm{.}81\frac{m}{s^2}.$

The EoM is given by:

$\frac{3}{2}m{x}^{}+(k_1+k_2)x=$mgsin$.$

a$)$ Write the EoM in standard form. Determine the

natural angular frequency of the system and the static

deformation $($i$.$e$.,$ the value of $x$ if there is no motion$).$

b$)$ Solve the EoM analytically with IC $x(0)=x_0=$

$-0\mathrm{.}1$ m and $x^{}(0)=0.$