Question: 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}

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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