Four pulleys, A, B, C and D, are mounted on a shaft. Due to poor manufacturing processes the centres of mass do not coincide with the shaft axis. The eccentricities and relative angular location of the mass centres, along with other pertinent data, are provided in the table. The shaft is supported in bearings E and F located 0.3 m and 1.2 m respectively to the right of pulley A. The shaft is to be dynamically balanced by the addition of balancing masses in balancing planes X and Y at radii of 200 and 300 mm respectively. Determine the magnitude of the balancing masses and their positions relative to the out-of-balance location of pulley A. Pulley Bearing A B D or X E F Y Mass (kg) 400 650 650 400 Eccentricity (mm) 7.5 5.5 6.0 4.5 Angular orientation (degrees) 0 35 90 150 (16 Marks) Axial position from A (m) 0 0.25 0.3 0.6 0.9 1.2 1.25 1.5 (b) (Not related to Part (a) above.) A circular cross-section prismatic bar is fixed on its left end and free on its right end (4 Marks) Sketch the mode shapes of transverse (bending) vibration of the lowest three modes, clearly showing the nodes. Total 20 Marks)