GATE ME topic:vibrations PYQs & Answers

Questions 1–10 of 27. Imported answers require independent review unless marked reviewed.

In a single degree of freedom vibrating system with only viscous damping, the critical damping coefficient is 350 N s/m and the damping coefficient is 35 N s/m.

The logarithmic decrement of the vibrating system is

Your answerChoose one option.

0.63

1.26

0.32

1.89

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A 5 kg mass is suspended at the free end of an overhanging massless beam, having a pin support and a roller support, as shown in the figure below. Young’s modulus of the material of the beam is 200 GPa and moment of inertia of the beam is

. The natural frequency of the beam in rad/s is

Diagram for Mechanical Engineering question 42

Your answerChoose one option.

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A block of mass 1 kg connected to a spring of stiffness 10 N m

is operating in a viscous medium such that the damping ratio (or damping factor) is equal to the ratio of the damped frequency to the natural frequency. The magnitude of the damping ratio for this system is ________ (rounded off to 2 decimal places).

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The system shown in the figure below consists of a cantilever beam (with flexural rigidity

and negligible mass), a spring (with spring constant

and negligible mass) and a block of mass

. Assuming a lumped parameter model for the system, the fundamental natural frequency (

) of the system is

Your answerChoose one option.

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A linear spring-mass-dashpot system with a mass of 2 kg is set in motion with viscous damping. If the natural frequency is 15 Hz, and the amplitudes of two successive cycles measured are 7.75 mm and 7.20 mm, the coefficient of viscous damping (in N.s/m) is

Your answerChoose one option.

4.41

7.51

2.52

6.11

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A vibratory system consists of mass

, a vertical spring of stiffness

and a horizontal spring of stiffness

. The end A of the horizontal spring is given a horizontal motion

. The other end of the spring is connected to an inextensible rope that passes over two massless pulleys as shown. Assume

kg,

kN/m, and neglect friction. The magnitude of critical driving frequency for which the oscillations of mass

tend to become excessively large is ________ rad/s (answer in integer).

Diagram for Mechanical Engineering question 55

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The figure shows a block of mass m = 20 kg attached to a pair of identical linear springs, each having a spring constant k = 1000 N/m. The block oscillates on a frictionless horizontal surface. Assuming free vibrations, the time taken by the block to complete ten oscillations is ________ seconds. (Rounded off to two decimal places)

Take π = 3.14.

Diagram for Mechanical Engineering question 30

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For a dynamical system governed by the equation,

the damping ratio

is equal to

. The displacement

of this system is measured during a hammer test. A displacement peak in the positive displacement direction is measured to be 4 mm. Neglecting higher powers (>1) of the damping ratio, the displacement at the next peak in the positive direction will be ______ mm (in integer).

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Consider a forced single degree-of-freedom system governed by

, where

and

are the damping ratio and undamped natural frequency of the system, respectively, while

is the forcing frequency. The amplitude of the forced steady state response of this system is given by

, where

. The peak amplitude of this response occurs at a frequency

. If

denotes the damped natural frequency of this system, which one of the following options is true?

Your answerChoose one option.

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A spring mass damper system (mass

, stiffness

, and damping coefficient

) excited by a force

, where

and

are the amplitude, frequency and time, respectively, is shown in the figure. Four different responses of the system (marked as (i) to (iv)) are shown just to the right of the system figure. In the figures of the responses,

is the amplitude of response shown in red color and the dashed lines indicate its envelope. The responses represent only the qualitative trend and these are not drawn to any specific scale.

Four different parameter and forcing conditions are mentioned below.

(P)

and

(Q)

and

(R)

and

(S)

and

Which one of the following options gives correct match (indicated by arrow →) of the parameter and forcing conditions to the responses?

Diagram for Mechanical Engineering question 40

Your answerChoose one option.

(P) → (i), (Q) → (iii), (R) → (iv), (S) → (ii)

(P) → (ii), (Q) → (iii), (R) → (iv), (S) → (i)

(P) → (i), (Q) → (iv), (R) → (ii), (S) → (iii)

(P) → (iii), (Q) → (iv), (R) → (ii), (S) → (i)

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GATE ME topic:vibrations PYQs

How to practice topic:vibrations

Question 18

Question 42

Question 35

Question 42

Question 25

Question 55

Question 30

Question 31

Question 39

Question 40