In this article we will bring you videos on previous GATE Mechanical Questions on the subject of Mechanical Vibrations. Feel free to share any queries that you may have on the solutions. 

Q1) 1. The rotor shaft of a large electric motor supported between short bearings at both the ends shows a deflection of 1.8 mm in the middle of the rotor. Assuming the rotor to be perfectly balanced and supported at knife edges at both the ends, the likely critical speed (in rpm) of the shaft is
a. 350
b. 705
c. 2810
d. 4430

Solution:

Q2) A concentrated mass m is attached at the centre of a rod of length 2L as shown in the figure. The rod is kept in a horizontal equilibrium position by a spring of stiffness k. For very small amplitude of vibration, neglecting the weights of the rod and spring, the undamped natural frequency of the system is 

a. 

b. 

c. 

d. 

Solution:

Q3) An automotive engine weighing 240 kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of 16 MN/m while the stiffness of each rear spring is 32 MN/m. The engine seed (in rmp), at which resonance is likely to occur, is

a. 6040

b. 3020

c. 1424

d. 955

Solution:

Q4) As shown in figure, a mass of 100 kg is held between two springs. The natural frequency of vibration of the system, in cycles/s, is 

a. 

b. 

c. 

d. 

Solution:

Q5) In a spring-mass system, the mass is m and the spring constant is k. The critical damping coefficient of the system is 0.1 kg/s. In another spring-mass system, the mass is 2m and the spring constant is 8k. The critical damping coefficient (in kg/s) of this system is _________

a. 0.6

b. 0.3

c. 0.4

d. 0.8

Solution:

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