GATE AE topic:structural-dynamics PYQs & Answers

Questions 1–10 of 28. Imported answers require independent review unless marked reviewed.

The response

of a freely vibrating single degree of freedom underdamped system is given below. In the equation, A and

are constants. The damping ratio of the system is ________ (rounded off to 3 decimal places).

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A system comprising a bar, spring and mass is shown in the figure below. The bar, having negligible mass, is made of a material having Young’s modulus

GPa, cross-sectional area

mm², and length

mm. The spring stiffness

kN/mm and the mass

kg. The natural frequency of free vibration of the system is ________ rad/s (rounded off to the nearest integer).

Diagram for Aerospace Engineering question 59

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A uniform rigid bar of mass 3 kg is hinged at point F, and supported by a spring of stiffness k=100 N/m, as shown in the figure.

Diagram for Aerospace Engineering question 57

The natural frequency of free vibration of the system is ____ rad/s (answer in integer).

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Consider the free vibration responses P, Q, R and S (shown in the figure) of a single degree of freedom spring-mass-damper system with the same initial conditions. For the different damping cases listed below, which one of the following options is correct?

Overdamped

Underdamped

Critically damped

Undamped

Diagram for Aerospace Engineering question 14

Your answerChoose one option.

P – 1, Q – 4, R – 2, S – 3

P – 1, Q – 2, R – 4, S – 3

P – 3, Q – 4, R – 2, S – 1

P – 3, Q – 2, R – 4, S – 1

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For a single degree of freedom spring-mass-damper system subjected to harmonic forcing, the part of the motion (response) that decays due to damping is known as:

Your answerChoose one option.

transient response

steady-state response

harmonic response

non-transient response

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The equations of motion for a two degrees of freedom undamped spring-mass system are:

where m and k represent mass and stiffness respectively, in corresponding SI units, and

and

are the degrees of freedom. The larger of the two natural frequencies is given by:

rad/s. The value of

is ________ (rounded off to 2 decimal places).

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Which of the following statement(s) is/are true about harmonically excited forced vibration of a single degree-of-freedom linear spring-mass-damper system?

Your answerSelect all correct options. You can choose more than one.

The total response of the mass is a combination of free vibration transient and steady-state response.

The free vibration transient dies out with time for each of the three possible conditions of damping (under-damped, critically damped, and over-damped).

The steady-state periodic response is dependent on the initial conditions at the time of application of external forcing.

The rate of decay of free vibration transient response depends on the mass, spring stiffness and damping constant.

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For studying wing vibrations, a wing of mass

and finite dimensions has been idealized by assuming it to be supported using a linear spring of equivalent stiffness

and a torsional spring of equivalent stiffness

as shown in the figure. The centre of gravity (CG) of the wing idealized as an airfoil is marked in the figure. The number of degree(s) of freedom for this idealized wing vibration model is ________. (Answer in integer)

Diagram for Aerospace Engineering question 30

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A single degree-of-freedom spring-mass-damper system has viscous damping ratio of 0.1. The mass is given an initial displacement of 10 cm without imparting any velocity. After exactly two complete cycles of oscillation (i.e., after time

, where

is the period of the damped vibration), the amplitude of the displacement is _____ cm. (round off to two decimal place)

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A damper with damping coefficient,

, is attached to a mass of 5 kg and spring of stiffness 5 kN/m as shown in figure. The system undergoes under-damped oscillations.

If the ratio of the 3rd amplitude to the 4th amplitude of oscillations is 1.5, the value of

is ____ Ns/m (rounded off to the nearest integer).

Diagram for Aerospace Engineering question 62

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GATE AE topic:structural-dynamics PYQs

How to practice topic:structural-dynamics

Question 33

Question 59

Question 57

Question 14

Question 15

Question 55

Question 25

Question 30

Question 51

Question 62