The free end of the piston of Chapter Problem 10.16 is subject to a force \(1000 \sin \omega t \mathrm{~N}\), where \(\omega=100 \mathrm{~Hz}\). If the diameter of the shaft is \(8 \mathrm{~cm}\), determine the steady-state response of the piston.

Data From Chapter Problem 10.16:

A large industrial piston operates at \(1000 \mathrm{~Hz}\). The piston head has a mass of \(20 \mathrm{~kg}\). The shaft is made from steel \(\left(ho=7500 \mathrm{~kg} / \mathrm{m}^{3}, E=210 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\right)\).