Athin disk of mass 350 grams and radius 10 mm is attached to the end of a circular shaft of length 20 cm, radius 3 mm that is made from a material of elastic modulus l 50x10' n/m. and shear modulus 50x10, n/m2. what are the (a) natural frequency for longitudinal motion of the disk, (b) natural frequency for torsional oscillation of the disk and (c) natural frequency for transverse motion of the disk. assume the shaft is massless in all cases.
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