Question 1
Show or otherwise that for a single rotor system, the natural frequency of vibration can be expressed as w n = √(Gj/IL)
A steel disc 300 mm diameter, of mass 29 kg is suspended from the end of a wire 2.5 mm diameter and 1.5 m long which is clamped into a control hole in the disc, the upper end of the wire being rigidly supported. When the disc is set in torsional vibration, it is found to make 10 complete oscillations on 78.2 seconds. Find the modulus of rigidity of the wire, and calculate the amplitude of the oscillation which may be allowed if the maximum permissible intensity of shearing stress in the wire is 140 MN/m2 .(hint take I = mR2 /2; where R is the radius of the disc).
Question 2
Show that the deflection of shaft from the static deflection position at any speed, w, in terms of the critical speed is given as y = (w 2 e)/(wc 2 - w2 )
A shaft, 12 mm diameter, rotates in spherical bearing with a span of 0.9 m and carries a disc of mass 12 kg midway between the two bearings
Neglecting the mass of the shaft, determine the deflection of the shaft in terms of it's speed of rotation in radians per second, if the mass-center of the disc is 0.25 mm out of center. If the stress in the shaft is not to exceed 100MN/m 2 , determine the range of the speed within which it is unsafe to run the shaft.(hint:take E=200GN/m 2 )
Question 3
Derive equations for determining the torque required to raise and lower a load using a screw jack. What is the condition for self locking of the screw jack?
The mean diameter of a square threaded screw jack is 50 mm. The pitch of of the thread is 10 mm. The coefficient of friction is 0.15. What force must be applied at the end of a 0.7 m long lever, which is perpendicular to the longitudinal axis of the screw to raise a load of 20 kN and to lower it?.
Question 4
Derive equation to determine the torque which is transmitted by a single disc clutch which has both sides effective
A single plate clutch, which has both side effective, has outer and inner diameters 300 mm and 200 mm respectively. The maximum intensity of pressure at any point on the contact surface is not to exceed 0.1 N/mm2 . if the coefficient of friction is 0.3, determine the power transmitted by a clutch at a speed of 2500 rpm
Question 5
Derive expressions for the efficiency of an inclined plane when a body is moving down the plane and up the plane
An effort of 1500 N is required to just move a certain body up an inclined plane of angle 12o , force acting parallel to the plane. If the angle of inclination is increased to 15o , then the effort required is 1720 N. find the weight of the body and the coefficient of friction
Question 6
Consider a shaft AB fixed at both ends and carrying as uniformly distributed load of w per unit length as show in fig. Q6 show that the natural frequency of free transverse vibration of the shaft is fn = 3.573√(g/384ds
A flywheel is mounted on a vertical shaft as shown in fig 23.8. The both ends of the shaft are fixed and its diameter is 50mm. the flywheel has a mass of 500 kg. Find the natural frequencies of longitudinal and transverse vibrations. Take E=200GN/m 2
Question 7
The differential equation for the mass-spring-damper system of the model in fig. Q7 is given as
my'' + cy' +ky = 0
obtain the solutions of the equation when there is
(I) no external force on the system
(ii) external force on the system
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