1
GATE ME 2024
Numerical
+2
-1.33
A vibratory system consists of mass $m$, a vertical spring of stiffness $2k$ and a horizontal spring of stiffness $k$. The end $A$ of the horizontal spring is given a horizontal motion $x_A = a \sin \omega t$. The other end of the spring is connected to an inextensible rope that passes over two massless pulleys as shown.
Assume $m = 10 kg$, $k = 1.5$ kN/m, and neglect friction.
The magnitude of critical driving frequency for which the oscillations of mass $m$ tend to become excessively large is _____ rad/s (answer in integer).
![GATE ME 2024 Theory of Machines - Vibrations Question 1 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lx72qtvm/344f0fe8-4fa7-4f37-b0aa-a0dd0cc0372a/fa624a20-261c-11ef-a279-4f9760cfcb83/file-6y3zli1lx72qtvn.png?format=png)
Your input ____
2
GATE ME 2017 Set 2
Numerical
+2
-0
The radius of gyration of a compound pendulum about the point of suspension is $$100$$ mm. The distance between the point of suspension and the centre of mass is $$250$$ mm. Considering the acceleration due to gravity as $$9.81$$ m/s2, the natural frequency (in radian/s) of the compound pendulum is _________.
Your input ____
3
GATE ME 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
A thin uniform rigid bar of length $$L$$ and mass $$M$$ is hinged at point $$O,$$ located at a distance of $${L \over 3}$$ from one of its ends. The bar is further supported using springs, each of stiffness $$k,$$ located at the two ends. A particle of mass $$m = {m \over 4}$$ is fixed at one end of the bar, as shown in the figure. For small rotations of the bar about $$O,$$ the natural frequency of the systems is
![GATE ME 2017 Set 1 Theory of Machines - Vibrations Question 7 English](https://gateclass.cdn.examgoal.net/mfqAIlexhVZDA99NR/ZMiO2TIVfpWih3VD9ot3bx1oOUJoL/9oFzl6bCMT858WI0Q4pCRC/uploadfile.jpg)
4
GATE ME 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
A solid disc with radius a is connected to a spring at a point $$d$$ above the center of the disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of the disc is $$M$$ and the spring constant is $$K$$. The polar moment of inertia for the disc about its centre is $$J = {{M{a^2}} \over 2}$$
![GATE ME 2016 Set 1 Theory of Machines - Vibrations Question 8 English](https://gateclass.cdn.examgoal.net/X3Vip4JfkUnTuPbHS/VxgcgzPnyH6y5yZw0wegSjGej8ghv/U5i1Nom7NI63MlPQCO3BAK/uploadfile.jpg)
The natural frequency of this system in rad/s is given by
Questions Asked from Vibrations (Marks 2)
Number in Brackets after Paper Indicates No. of Questions
GATE ME 2024 (1)
GATE ME 2017 Set 2 (1)
GATE ME 2017 Set 1 (1)
GATE ME 2016 Set 1 (1)
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GATE ME Subjects
Engineering Mechanics
Machine Design
Strength of Materials
Heat Transfer
Production Engineering
Industrial Engineering
Turbo Machinery
Theory of Machines
Engineering Mathematics
Fluid Mechanics
Thermodynamics
General Aptitude