Problem $2$ A rotating machine of mass $M=120kg$ has an unbalanced mass $m=0\mathrm{.}2kg$ a distance $r=0\mathrm{.}5m$ from the center of rotation. $($The mass M includes mass m$.)$ The operating speed is $10$ Hz $.$ Suppose that the machine is mounted on an isolator consisting of a spring and damper, as shown in the figure below. If it is desired that $$ be $0\mathrm{.}25,$ specify the spring constant $k$ such that only $5\%$ of the excitation force is transmitted to the foundation. Also, determine the amplitude of the transmitted force.