GATE AE topic:structural-dynamics PYQs & Answers — Page 2

Questions 11–20 of 28. Imported answers require independent review unless marked reviewed.

A uniform rigid prismatic bar of total mass

is suspended from a ceiling by two identical springs as shown in figure.

Let

and

be the natural frequencies of mode I and mode II respectively (

The value of

is ________ (rounded off to one decimal place).

Diagram for Aerospace Engineering question 63

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A single degree of freedom spring-mass-damper system is designed to ensure that the system returns to its original undisturbed position in minimum possible time without overshooting. If the mass of the system is 10 kg, spring stiffness is 1740 N/m and the natural frequency is 13.2 rad/s, the coefficient of damping of the system in Ns/m is ______ (round off to nearest integer).

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Two cantilever beams (Beam 1 and Beam 2) are made of same homogenous material and have identical cross sections. Beam 1 has length

and Beam 2 has length

. Ratio of the first natural frequency of Beam 1 to that of Beam 2 is ______ (round off to nearest integer).

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A rigid massless rod pinned at one end has a mass

attached to its other end. The rod is supported by a linear spring of stiffness

as shown in the figure.

The natural frequency of this system is:

Diagram for Aerospace Engineering question 26

Your answerChoose one option.

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A two degree of freedom spring-mass system undergoing free vibration with generalized coordinates

and

has natural frequencies

rad/s and

rad/s, respectively. The corresponding mode shapes are

and

. If the system is disturbed with certain deflections and zero initial velocities, then which of the following statement(s) is/are true?

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

An initial deflection of

cm and

cm would make the system oscillate with only the second natural frequency.

An initial deflection of

cm and

cm would make the system oscillate with only the first natural frequency.

An initial deflection of

cm and

cm would make the system oscillate with a linear combination of first and second natural frequencies.

An initial deflection of

cm and

cm would make the system oscillate with only the first natural frequency.

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The natural frequency of the first mode of a rectangular cross section cantilever aluminum beam is

rad/s. If the material and cross-section remain the same, but the length of the beam is doubled, the first mode frequency will become

Your answerChoose one option.

rad/s

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A critically damped single degree of freedom spring-mass-damper system used in a door closing mechanism becomes overdamped due to softening of the spring with extended use. If the new damping ratio (

) for overdamped condition is 1.2, the ratio of the original spring stiffness to the new spring stiffness (

), assuming that the other parameters remain unchanged, is ______ (round off to two decimal places).

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The two masses of the two degree of freedom system shown in the figure are given initial displacements of 2 cm (

) and 1.24 cm (

). The system starts to vibrate in the first mode. The first mode shape of this system is

, where

______ (round off to two decimal places).

Diagram for Aerospace Engineering question 52

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In the spring-mass system, shown in the figure, mass

kg and the spring stiffness

kN/m. The natural frequency of the system is ______ Hz (round off to the nearest integer).

Diagram for Aerospace Engineering question 25

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For a damped spring-mass system, mass

kg, stiffness

N/m, and damping coefficient

kg/s. The ratio of the amplitude of oscillation of the first cycle to that of the fifth cycle is _____ (round off to 1 decimal place).

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GATE AE topic:structural-dynamics PYQs

Question 63

Question 19

Question 20

Question 26

Question 32

Question 18

Question 51

Question 52

Question 25

Question 54