Answer ALL questions
PART A – (10×2=20 marks)
1.            Differentiate between static and dynamic equilibrium.
2.            Define inertia force.
3.            Can a single cylinder engine be fully balanced?  Why?
4.            What are the effects of hammer blow and swaying couple?
5.            What are the various types of damping?
6.            Define magnification ratio.
7.            What is meant by sensitivity of a governor?
8.            What is the effect of friction on the governors?
9.            Define gyroscopic couple.
10.        What is meant by automatic controls?


PART B – (5x16=80 marks)
11.        (a)  A machine weighing 75 kg is mounted on springs and is fitted with dashpot to damp vibrations.  There are three springs each of stiffness 10 kg / cm and it is found that the amplitude of vibration diminishes from 3.84 cm to 0.64 cm in two consecutive oscillations.  Assuming damping force varies as the velocity, determine the resistance of the dashpot at unit velocity and compare the frequency of damped vibration with the frequency when the dashpot is not in operation.
(or)
(b) A vertical single cylinder gas engine has a bore of 8 cm and a stroke of 10 cm.  the connecting rod length is 20 cm and the reciprocating parts weigh 1.5 kg.  The gas pressure on the piston is 6 kg/cm2 when it has moved 1.5 cm from the inner dead centre on its power stroke.  Determine the net load on the gudgeon pin when engine runs at 2000 rpm.  At what speed this load will be zero?

12     (a). The turning moment curve for an engine is represented by the equation, T = (20000 + 9500 sin 2q - 5700 cos 2q) N-m, where q is the rotation of the crank.  If the resisting torque is constant, find
i. Power developed
ii. M.I of the flywheel; and
                  iii. angular acceleration of the flywheel at 450 of crank rotation from I.D.C
iv. the speed of the engine is 180 r.p.m and total fluctuation of speed is 1%.
(or)
(b). The four cylinders A, B, C, D of a vertical engine are spaced at 24 cm, 11 cm and 24 cm centers.  The reciprocating masses of cylinders A and D each weigh 160 kg and their cranks are 900 to one another.  The stroke is 12 cm and connecting rod length is 20 cm.  Determine the weights of reciprocating masses for B and C and their crank position relative to A if all the primary forces and couples are balanced one another.  Calculate maximum unbalanced secondary force when the engine is running at 450 r.p.m.
13     (a). A, B, C and D are four masses carried by a rotating shaft at radii 100, 125, 200 and 150 mm respectively.  The planes in which the masses revolve are spaced 600 mm apart and the masses of B, C and D are 10 kg and 4 kg respectively.  Find the required mass A and the relative angular settings of the four masses so that the shaft shall be in complete balance.
(or)
(b). Determine the natural frequency of oscillations of the system by energy method and also by Newton’s method.
14     (a) The two equal masses of 500 kg and radius of gyration 37.5 cm are  keyed to opposite ends of a shaft 60 cm long.  The shaft is 7.5 cm dia for the first 25 cm and 12.5 cm dia for the next 10 cm and 8.75 cm dia. For the remainder of its length.  Find the natural frequency of the free torsional vibration of the system and the position of the node.  Take G = 8 x 106 N/cm2.
(or)
(b). A motor cycle with its rider weighs 250 kg., the centre of gravity of the machine and the rider combined being 60 cm above the ground level when the machine is standing upright.  Each road wheel has a moment of inertia of 8 kg – m and rolling diameter of 60 cm.  the engine rotates six times the speed of the road wheels in the same sense.  The moment of inertia of engine is 1.5 kg m2.  Determine the angle of wheel necessary if the motor cycle is traveling at a speed of 15 m/sec in a curve of 30 m.
15     (a) The controlling force FC and radius of rotation of a spring controlled governor is given by the expression. 
         FC = 2000r – 76
         The mass of the ball is 5 kg and extreme radii of rotation of the ball are 0.1m and 0.175m respectively for max. and min speeds.  If the friction on the governor is 5 N at each ball find the coefficient of insensitiveness of the governor at extreme radii.
(or)
         (b) A governor of the proell type has each arm 250mm long.  The pivots of the upper and lower arms are 25 mm from the axis.  The central load acting on the sleeve has a mass of 25 kg and them  each rotating ball has a mass of 3.2 kg.  When the governor sleeve is in mid – position, the extension link of the lower arm is vertical and the radius of the path of rotation of the masses is 175 mm.  The vertical height of the governor is 200 mm.

         If the governor speed is 160 r. p. m when in mid – position, find : 1. length of the  extension link; and 2. tension in the upper arm.