1.a. State condition for static equilibrium of body subjected to a system

1.two forces

2.three forces

3.member with two forces and a torque.

1.b. For the 4 bar mechanism shown find required torque T2 and various P in forces on links for equilibrim of the system.

2.a. Explain D'Almerts principle and state its significance.

2.b. In a vertical double acting steam engine,the connecting rod is 4.5 times the crank The weight of the reciprocating parts is 120kg and stroke of piston is 440mm The engine runs at 250rpm.If the net load on the piston due to steam pressure is 25kN when the crank has turned through an angle of 120° from the top dead centre

1.Thrust in the connecting rod

2.Pressure on slide bars

3.Tangential force on the crank pin

4.Thrust on bearings.

5.Turning moment on the crank shaft.

3.a. A,B,C,D are masses carried by a roating shaft at radii 100,125,200 and 150mm respectively .The planes in which the masses revolve are spaced 600mm apart and the mass respectively.Find the required mass A and the relative angular settings of the $ massses so that the shaft shall be in complete balance.

3.b. What do you mean by static and dynamic balancing?

4. A four crank engine has the two outer cranks set at 120° to each other and their reciprocating masses are each 400kg.The distance between the planes of rotation of adjacent cranks are 450mm,750mm and 600mm.If the engine is to be in complete primary balance find the reciprocating mass and the relative angular position for each of the inner cranks .If the length of length of each crank is 300mm the length of each connecting rod is 1.2 and the speed of rotation is 240rpm.What is the maximum secondary unbalanced force?

5.a. Explain the following

1.Stability

2.Sensitiveness

3.Isochronism

4.Hunting.

5.b. A porter governor has equal arms each 250 mm long and pivoted on the axis of rotation.Each ball has a mass of 5kg and the mass of central load on sleeve is 25kg The radius of rotation of the ball is 150mm when the governor begins to lift and 200mm when the governor is at maximum speed.Find the minimum and maximum speed and range of speed of the governor.

6.a. With neat sketches explain the effect of gyroscopic couple on steering ,pitching and rolling of a ship.

6.b. An aeroplane flying at 240km/h turns to ward the left and completes a quater circle of 60m radius .The mass of the rotor engine and propeller of the plane is 450kg with a radius of gyration of 320mm . The engine speed is 200 rpm clockwise when viewed from the rear determine the gyroscope couple on the aircraft and its effect.In what way is the effect changed when the

1.Aeroplane turns towards right.

2.Engine rotates clockwise when viwed from the front (nose end) and the aeroplane turns left and right.

7.a. Add the following harmonic motions analytically and check solution graphically.

7.b. Find natural frequency of the system using energy method.

8.a. Find natural frequency of the system using newton's method.

8.b. Find natural frequency of the system shown

9.a. Set up differential equation for a spring mass damper system and obtain complete solution for critically damped condition.

9.b. Determine:

1.Critical damping coefficient 2.Damping factor 3.Natural frequency of damped vibrations. 4.Logarithmic decrement. 5.Ratio of two consective amplitude of vibrating system which consists of mass of 25kg,a spring of stiffiness 15kN/m and a damper.The damping provided is only 15% of critical value.

10.a. Define transmissibilty and derive an expressiion for the transmissiblity ratio and the phase angle for transmitted force.

10.b. A machine of mass one ton is acted upon by an external force 2450N at a frequency of 1500 rpm.To reduce the effects of vibration ,isolator abd rubber having a static deflection of 2mm under the machine load and an estimated damping factor of 0.2 are used Determine.

1.Force transmitted to the foundation.

2.Amplitude of vibration og the machine.

3.Phase lag of the transmitted force with respect to external force.