$(30$ Points$)$ The $2$ DOF rotating mass model below features a $60$ kg rotor with a mass

unbalance level of $U_u=3\mathrm{.}0kg*mm.$

a$.$ Specify the horizonal and vertical stiffness coefficients, $k_x$ and $k_y,$ such that the

horizontal and vertical natural frequencies are calculated as $5000$ rpm and

$9000$ rpm $,$ respectively.

b$.$ Specify the horizonal and vertical damping coefficients, $c_x$ and $c_y,$ such that the

horizontal and vertical damping ratios are calculated as $8\%$ and $5\%,$ respectively.

c$.$ Calculate the orbit ellipse properties $($i$.$e$.$ semi$-$major axis, semi$-$minor axis, and

attitude angle$)$ at a running speed of $4900$ rpm $.$ Is the orbit forward whirling or

backward whirling at this speed?

d$.$ Provide a single plot of the circular forward and backward whirling components

of the orbit as well as the overall elliptical rotor orbit.