A vibration isolator system is designed for a machine that has a rotating unbalanced mass of m at a distance of $0\mathrm{.}19$ m from the axis of rotation and operates at a speed of $25$ rad$/$s$,$ as shown in the figure. The vibration isolator has negligible damping and a stiffness of $365$ kN$/$m$,$ and the machine has a mass of $100$ kg$.$ Determine the minimum unbalanced mass m so that the maximum force transmitted to the foundation is not more than $2\mathrm{.}2$ kN$.$ Give your answer in grams. Work to $3$ decimal places and do not include the units when submitting the answer.