The propeller of a ship is a tapered circular cylinder, as shown in Figure P2.24. When installed in the ship, one end of the propeller is constrained from longitudinal motion relative to the ship while a \(500-\mathrm{kg}\) propeller mass is attached to its other end.

(a) Determine the equivalent longitudinal stiffness of the shaft for a SDOF model.

(b) Assuming a linear displacement function along the shaft, determine the equivalent mass of the shaft to use in a SDOF model.

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FIGURE P 2.24 10 m r = 30 cm r = 20 cm E 210 x 10 N/m p=7850 kg/m