$(3$ pts$)$ Problem $3$:

A rotating machine has an unbalanced mass of $3$ kg at a distance $0\mathrm{.}12$ m from the center of rotation. The mass of the machine without adding the unbalance mass is $90$ kg $.$ The operating speed is $12$ Hz $.$ Suppose the machine is mounted on an isolator consisting of a spring and damper, as shown. The damping ratio is desired to be $0\mathrm{.}15,$ find:

$1-(2$ pts$)$ The spring constant $\backslash ($ k $\backslash )$ such that only $\backslash (25\backslash \%\backslash )$ of the excitation force is transmitted to the foundation.

$2-(1$ pt$)$ The amplitude of the transmitted force