This question has THREE parts: $($a$)($b$)($b$)$ and $($c$)\_$

Question is missing tests or variants.

The following system is composed by

two identical masses $($each of mass $m=60kg)$ constrained to move horizontally.

a disc of mass $m=60kg,$ moment of inertia $I_C=19\mathrm{.}0kg*m^2($about its centre $C,$ which is also its

centre of gravity$)$ and radius $r=0\mathrm{.}53m.$ The disc is rotates about its centre $C.$

The disc is connected to the ground by a torsional spring with torsional stiffness $k_t=$

$1300N*\frac{m}{r}ad.$ The mass on the left is connected to top of the disc by an inextensible cable

which rolls on the disc without slipping. The mass on the right is connected to the bottom of the

disc by a flexible cable of stiffness $k=1100\frac{N}{m},$ which rolls without slipping on

disc. For $x_1=x_2==0($as in figure$),$ all springs are unstretched.

$($a$)$ Using the coordinate vector $x=[x_1{x}_2{]}^{TT},$ find the numerical values of the mass and stiffness matrices of the

system in SI units.

$($b$)$ Find the natural frequencies and mode shapes of the system in numerical form.

$($c$)$ Draw the mode shapes of the system. This part is to be answered only on your handwritten solutions.