1) In the reverted epicyclic train, arm F carries two wheels A and D and a compound wheel B-C. Wheel A meshes with wheel B and wheel D meshes with wheel C. Numbers of teeth on wheel A, D and C are 80, 48 and 72 respectively. Determine the speed and direction of wheel D when wheel A is fixed and arm F, makes 200 rpm, clockwise.
2) A, B, C and D are four masses carries by the rotating shaft at radii of 100mm, 125mm, 200mm and 150mm respectively. Planes in which masses revolve are placed at a distance of 600mm mm apart and the masses B, C and D are 10 kg, 5kg and 4kg respectively. Determine the mass of A and angular settings of four masses so that the shaft is in complete balance.
3) A four cylinder vertical engine has cranks 300mm long. Planes of rotation of first, third and fourth cranks are 750mm, 1050mm and 1650mm respectively form that of the second crank and their reciprocating masses are 150kg, 400kg and 250kg respectively. Determine the mass of reciprocating parts for second cylinder and relative angular positions of cranks in order that the engine may be in complete primary balance.
4) Shaft of 100mm diameter and 1 meter long is fixed at one end and other carries a flywheel of mass one tonne. By taking Young’s modulus of shaft materials as 200GN/m^{2}, determine the natural frequency of longitudinal and tansverse vibration.
5) Machine of mass 100 kg is supported on the openings of total stiffness 800 kN/m and has the rotating unbalanced element that results in the disturbing force of 40N at a speed of 300 rpm. Supposing the damping ratio as 0.25, find out:
(a) Amplitude of vibrations due to unbalance and
(b) Transmitted force