GATE ME topic:vibrations PYQs & Answers — Page 2

Questions 11–20 of 27. Imported answers require independent review unless marked reviewed.

Consider a single degree of freedom system comprising a mass

, supported on a spring and a dashpot as shown in the figure.

Diagram for Mechanical Engineering question 25

If the amplitude of the free vibration response reduces from 8 mm to 1.5 mm in 3 cycles, the damping ratio of the system is ______ (round off to three decimal places).

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A tapet valve mechanism in an IC engine comprises a rocker arm ABC that is hinged at B as shown in the figure. The rocker is assumed rigid and it oscillates about the hinge B. The mass moment of inertia of the rocker about B is

kg.m

. The rocker arm dimensions are

cm and

cm. A pushrod pushes the rocker at location A, when moved vertically by a cam that rotates at

rpm. The pushrod is assumed massless and has a stiffness of 15 N/mm. At the other end C, the rocker pushes a valve against a spring of stiffness 10 N/mm. The valve is assumed massless and rigid.

Diagram for Mechanical Engineering question 32

Resonance in the rocker system occurs when the cam shaft runs at a speed of ______ rpm (round off to the nearest integer).

Your answerChoose one option.

496

4739

790

2369

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A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness (

) and damper (damping factor,

) in parallel. The designer has the following four isolators:

kN/m,

Arrange the isolators in the ascending order of the force transmitted to the foundation.

Your answerChoose one option.

1-3-4-2

1-3-2-4

4-3-1-2

3-1-2-4

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Consider the system shown in the figure. A rope goes over a pulley. A mass,

, is hanging from the rope. A spring of stiffness,

, is attached at one end of the rope. Assume rope is inextensible, massless and there is no slip between pulley and rope.

Diagram for Mechanical Engineering question 34

The pulley radius is

and its mass moment of inertia is

. Assume that the mass is vibrating harmonically about its static equilibrium position. The natural frequency of the system is

Your answerChoose one option.

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A single-degree-of-freedom oscillator is subjected to harmonic excitation

as shown in the figure.

Diagram for Mechanical Engineering question 6

The non-zero value of

, for which the amplitude of the force transmitted to the ground will be

, is

Your answerChoose one option.

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The equation of motion of a spring-mass-damper system is given by

The damping factor for the system is

Your answerChoose one option.

0.25

0.5

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A rigid mass-less rod of length

is connected to a disc (pulley) of mass

and radius

through a friction-less revolute joint. The other end of that rod is attached to a wall through a friction-less hinge. A spring of stiffness

is attached to the rod at its mid-span. An inextensible rope passes over half the disc periphery and is securely tied to a spring of stiffness

at point C as shown in the figure. There is no slip between the rope and the pulley. The system is in static equilibrium in the configuration shown in the figure and the rope is always taut.

Diagram for Mechanical Engineering question 31

Neglecting the influence of gravity, the natural frequency of the system for small amplitude vibration is

Your answerChoose one option.

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The natural frequencies corresponding to the spring-mass systems I and II are

and

, respectively. The ratio

Your answerChoose one option.

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A slender uniform rigid bar of mass

is hinged at O and supported by two springs, with stiffnesses

and

, and a damper with damping coefficient

, as shown in the figure. For the system to be critically damped, the ratio

should be

Your answerChoose one option.

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A uniform thin disk of mass 1 kg and radius 0.1 m is kept on a surface as shown in the figure. A spring of stiffness

N/m is connected to the disk center A and another spring of stiffness

N/m is connected at point B just above point A on the circumference of the disk. Initially, both the springs are unstretched. Assume pure rolling of the disk. For small disturbance from the equilibrium, the natural frequency of vibration of the system is ______ rad/s (round off to one decimal place).

Diagram for Mechanical Engineering question 43

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GATE ME topic:vibrations PYQs

Question 25

Question 32

Question 33

Question 34

Question 6

Question 7

Question 31

Question 6

Question 32

Question 43