For the absorber designed in Chapter Problem 6.63, what is the minimum steady-state amplitude of the machine and at what speed does it occur?

Data From Chapter Problem 6.63:

A \(100 \mathrm{~kg}\) machine is placed at the midspan of a 2-m-long cantilever beam \(\left(E=210 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}, I=2.3 \times 10^{-6} \mathrm{~m}^{4}\right)\). The machine produces a harmonic force of amplitude 60,000 N. Design a damped vibration absorber of mass \(30 \mathrm{~kg}\) such that when hung from the beam at midspan, the steady-state amplitude of the machine is less than \(8 \mathrm{~mm}\) at all speeds between 1300 and \(2000 \mathrm{rpm}\).