Engineering Sciences
GATE XE Vibrations PYQs
Build your understanding with focused practice from past exam papers.
How to practice Vibrations
Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.
Questions 1–10 of 17. Imported answers require independent review unless marked reviewed.
Question 69
Open questionXE-DMCQ1 markNeeds review
A rigid block of mass
on a horizontal surface is connected to three springs each having spring constant
as shown in the figure.Which one of the following is the CORRECT natural frequency of the system?
Your answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 79
Open questionXE-DMCQ2 marksNeeds review
A spring of stiffness
is connected to the center of a homogeneous right circular cylinder of radius
placed on a horizontal surface as shown in the figure. The cylinder is assumed to be rolling without slipping.Considering small amplitude of oscillation, which one of the following options is the CORRECT natural frequency of the system?
Your answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 66
Open questionXE-DMCQ1 markNeeds review
Consider a spring-mass system with mass m and spring stiffness k as shown in the illustration. At time t=0, the mass is displaced by P units and the velocity of the mass is zero. The displacement of the mass, x(t), is measured from the equilibrium position.
Which one of the following functions represent x(t)?
Your answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 71
Open questionXE-DMSQ1 markNeeds review
The natural frequency of a spring-mass system is 10 rad/s.
Which of the following statements is/are CORRECT?
Your answerSelect all correct options. You can choose more than one.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 85
Open questionXE-DNAT2 marksNeeds review
A massless cantilever beam, with a tip mass m of 10 kg, is modeled as an equivalent spring-mass system as shown in the figure. The beam is of length L = 1 m, with a circular cross-section of diameter d = 20 mm. The Young’s modulus of the beam material is 200 GPa. The natural frequency of the spring-mass system is ____ Hz (rounded off to two decimal places).
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 69
Open questionXE-DMCQ1 markNeeds review
A mass M is hung from a frictionless, massless pulley. The pulley is suspended by using an inextensible, massless rope of which one end is directly fixed to a support, and the other end is connected to the support through a linear spring of stiffness constant k (see figure). The natural frequency of this system is
Your answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 71
Open questionXE-DMSQ1 markNeeds review
A spring mass system is shown in the figure below. Take the acceleration due to gravity as
. The static deflection due to weight and the time period of oscillations, respectively, are
Your answerSelect all correct options. You can choose more than one.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 76
Open questionXE-DMCQ2 marksNeeds review
A spring-mass system having a mass
and spring constant
, placed horizontally on a foundation, is connected to a vertically hanging mass
with the help of an inextensible string. Ignore the friction in the pulleys and also the inertia of pulleys, string and spring. Gravity is acting vertically downwards as shown. The natural frequency of the system in rad/s is 
Your answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 9
Open questionXE-DNAT1 markNeeds review
During an earthquake, a structure vibrates and the vibration can be assumed to be in simple harmonic motion at 5 Hz. At a measurement point, the RMS value of acceleration is 10 m/s². The approximate amplitude of motion (in mm) at this point (rounded off to two decimal places) is
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 15
Open questionXE-DMCQ2 marksNeeds review
A hammer of mass 1 kg is used to break an almond shell. The velocity time graph of the hammer during the impact duration is shown in the figure. The shape of force time graph is also given, which can be approximated as a triangle. A force of 300 N is required for breaking the shell, while a force of 200 N will not be able to break it, but just introduce a crack. Which one of the following events will happen?
Your answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer