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Q.2 A vertical shaft of 50mm diameter and 1.75m long is fixed at both ends. A flywheel is mounted on this shaft at a

Q.2 A vertical shaft of 50mm diameter and 1.75m long is fixed at both ends. A flywheel is mounted on this shaft at a distance of 1m from the top end. The flywheel weighs 5kN and its radius of gyration is 0.5m. Find the natural frequencies of longitudinal, transverse and torsional vibrations. Take E = 210GPa and G = 80GPa.

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