A rotating shaft carries four unbalanced masses 18 kg, 14 kg, 16 kg and 12 kg at radii 50 mm,
60 mm, 70 mm and 60 mm respectively. The 2nd, 3rd and 4th masses revolve in planes 80 mm,
160 mm and 280 mm respectively measured from the plane of the first mass and are angularly
located at 60°, 135° and 270° respectively measured clockwise from the first mass looking from
this mass end of the shaft. The shaft is dynamically balanced by two masses, both located at 50
mm radii and revolving in planes mid-way between those of 1st and 2nd masses and midway
between those of 3rd and 4th masses. Determine, graphically or otherwise, the magnitudes of
the masses and their respective angular positions.