The electric motor and its base have a combined mass of $M=34$ $kg$. Inside the motor there is an unbalanced rotor which can be modeled as seen at right. The base of the motor is constrained to move vertically. The motor is running at a constant speed $\omega=8$ $rad/s$. Each of the four springs has constant stiffness $k=189$ $N/m$. The mass of the imbalance, $m$ (included in the $34$ $kg$ total mass) is $m=0.8$ $kg$. What eccentricity of the imbalanced mass, $e$, would result in a steady state amplitude of the system of $X=10$ $mm$ (For the purpose of this problem, ignore the damper, $c=$0)? $e=$ $mm$