Q$7\mathrm{.}23$ A vibration isolator system is designed for a machine that has a rotating unbalanced

mass of $m$ at a distance of $0\mathrm{.}2$ m from the axis of rotation and operates at a speed of $80$

$ra\frac{d}{s}$ as shown in Figure $7\mathrm{.}40.$ The vibration isolator has negligible damping and a

stiffness of $450k\frac{N}{m},$ and the machine has a mass of $100$ kg $.$ Determine the minimum

unbalanced mass $m$ so that the force transmitted to the foundation is less than $2\mathrm{.}2$ kN

$0\mathrm{.}73kg$