A large industrial piston operates at (1000 mathrm{~Hz}). The piston head has a mass of (20 mathrm{~kg}).

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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 \(\left(ho=7500 \mathrm{~kg} / \mathrm{m}^{3}, E=210 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\right)\). For what shaft diameters will all natural frequencies be out of the range of 900 to \(1100 \mathrm{~Hz}\) ?

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