It is found that an exhaust fan, of mass \(80 \mathrm{~kg}\) and operating speed \(1000 \mathrm{rpm}\), produces a repeating force of \(10,000 \mathrm{~N}\) on its rigid base. If the maximum force transmitted to the base is to be limited to \(2000 \mathrm{~N}\) using an undamped isolator, determine

(a) the maximum permissible stiffness of the isolator that serves the purpose;

(b) the steady-state amplitude of the exhaust fan with the isolator that has the maximum permissible stiffness; and

(c) the maximum amplitude of the exhaust fan with isolation during start-up.