$(25$ pts$)$ Consider a typical unbalanced machine problem as given in the figure below with a machine mass of $120$ kg $,$ a mount stiffness of $736k\frac{N}{m},$ and a damping value of $500k\frac{g}{s}.$ The amplitude of the out$-$of$-$balance force is measured to be $374$ N at a running speed of $2,812re\frac{v}{m}in.$ Determine the amplitude of motion due to the out of balance. $($Hint: Start with a Free Body Diagram$)$