The armature of a variable-speed electric motor, of mass \(200 \mathrm{~kg}\), has an unbalance due to manufacturing errors. The motor is mounted on an isolator having a stiffness of \(10 \mathrm{kN} / \mathrm{m}\) and a dashpot having a damping ratio of 0.15.

(a) Find the speed range over which the amplitude of the fluctuating force transmitted to the foundation will be larger than the exciting force.

(b) Find the speed range over which the transmitted force amplitude will be less than \(10 \%\) of the exciting force amplitude.