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GATE Past Year Questions: Forced Vibration | Theory of Machines (TOM) - Mechanical Engineering PDF Download

Question for GATE Past Year Questions: Forced Vibration
Try yourself:The equation of motion for a spring-mass system excited by a harmonic force is
GATE Past Year Questions: Forced Vibration | Theory of Machines (TOM) - Mechanical Engineering
where M is the mass, K is the spring stiffness, F is the force amplitude and w is the angular frequency of excitation. Resonance occurs when w is equal to

[2018]

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Question for GATE Past Year Questions: Forced Vibration
Try yourself:The damping ratio for a viscously damped spring mass system, governed by the relationship
GATE Past Year Questions: Forced Vibration | Theory of Machines (TOM) - Mechanical Engineering
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Question for GATE Past Year Questions: Forced Vibration
Try yourself: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 GATE Past Year Questions: Forced Vibration | Theory of Machines (TOM) - Mechanical Engineering
GATE Past Year Questions: Forced Vibration | Theory of Machines (TOM) - Mechanical Engineering
The natural frequency of this system in rad/s is given by

[2016]

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Question for GATE Past Year Questions: Forced Vibration
Try yourself:A single degree of freedom mass-spring-viscous damper system with mass m, spring constant k and viscous damping coefficient q is critically damped. The correct relation among m, k, and q is

[2016]

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Question for GATE Past Year Questions: Forced Vibration
Try yourself:Which of the following statements are TRUE for damped vibrations?
P. For a system having critical damping, the value of damping ratio is unity and system does not undergo a vibratory motion.
Q. Logarithmic decrement method is used to determine the amount of damping in a physical system.
R. In case of damping due to dry friction between moving surfaces resisting force of constant magnitude acts opposite to the relative motion.
S. For the case of viscous damping, drag force is directly proportional to the square of relative velocity.

[2015]

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Question for GATE Past Year Questions: Forced Vibration
Try yourself:Consider a single degree of freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to the exciting force is

[2014]

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Question for GATE Past Year Questions: Forced Vibration
Try yourself:Critical damping is the

[2014]

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Question for GATE Past Year Questions: Forced Vibration
Try yourself:A mass of 1 kg is attached to two identical springs each with stiffness k = 20 kN/m as shown in the figure. Under frictionless condition, the natural frequency of the system in Hz is close to
GATE Past Year Questions: Forced Vibration | Theory of Machines (TOM) - Mechanical Engineering

[2011]

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Question for GATE Past Year Questions: Forced Vibration
Try yourself:A mass m attached to a spring is subjected to a harmonic force as shown in figure. The amplitude of the forced motion is observed to be 50 mm. The value of m (in kg) is​
GATE Past Year Questions: Forced Vibration | Theory of Machines (TOM) - Mechanical Engineering

[2010]

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Question for GATE Past Year Questions: Forced Vibration
Try yourself:A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is 3.6 kN/m and the damping constant of the damper is 400 Ns/m. If the mass is 50 kg, then the damping factor (d) and damped natural frequency (fn), respectively, are

[2009]

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Question for GATE Past Year Questions: Forced Vibration
Try yourself:An automotive engine weighing 240 kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of 16 MN/m while the stiffness of each rear spring is 32 MN/m. The engine speed (in rpm), at which resonance is likely to occur, is

[2009]

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Question for GATE Past Year Questions: Forced Vibration
Try yourself:A vibratory system consists of a mass 12.5 kg, a spring of stiffness 1000 N/m, and a dashpot with damping coefficient of 15 Ns/m.
The value of critical damping of the system is

[2006]

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Question for GATE Past Year Questions: Forced Vibration
Try yourself:The differential equation governing the vibrating system is
GATE Past Year Questions: Forced Vibration | Theory of Machines (TOM) - Mechanical Engineering

[2006]

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Question for GATE Past Year Questions: Forced Vibration
Try yourself:In a spring-mass system, the mass is 0.1 kg and the stiffness of the spring is 1 kN/m. By introducing a damper, the frequency of oscillation is found to be 90% of the original value. What is the damping coefficient of the damper?

[2005]

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Question for GATE Past Year Questions: Forced Vibration
Try yourself:There are four samples P, Q, R and S with natural frequencies 64,96,128 and 256 Hz, respectively. They are mounted on test setups for conducting vibration experiments. If a loud pure note of frequency 144 Hz is produced by some instrument, which of the samples will show the most perceptible induced vibration?

[2005]

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Question for GATE Past Year Questions: Forced Vibration
Try yourself:A mass m, of 20 kg is attached to the free end of a steel cantilever beam of length 1000 mm having a cross-section of 25 × 25 mm. Assume the mass of the cantilever to be negligible and Esteel = 200 GPa. If the lateral vibration of this system is critically damped using a viscous damper, the damping constant of the damper is​

[2004]

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Question for GATE Past Year Questions: Forced Vibration
Try yourself:A uniform rigid slender bar of mass 10 kg, hinged at the left end is suspended with the help of spring and damper arrangement as shown in the figure where K= 2 kN/m, C = 500 Ns/m and the stiffness of the torsional spring kq is 1 kN /m/rad. Ignore the hinge dimensions.
GATE Past Year Questions: Forced Vibration | Theory of Machines (TOM) - Mechanical Engineering
The damping coefficient in the vibration equation is given by

[2003]

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Question for GATE Past Year Questions: Forced Vibration
Try yourself:A uniform rigid slender bar of mass 10 kg, hinged at the left end is suspended with the help of spring and damper arrangement as shown in the figure where K= 2 kN/m, C = 500 Ns/m and the stiffness of the torsional spring kq is 1 kN /m/rad. Ignore the hinge dimensions.​The undamped natural frequency of oscillations of the bar about the hinge point is
GATE Past Year Questions: Forced Vibration | Theory of Machines (TOM) - Mechanical Engineering

[2003]

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FAQs on GATE Past Year Questions: Forced Vibration - Theory of Machines (TOM) - Mechanical Engineering

1. What is forced vibration in mechanical engineering?
Ans. Forced vibration in mechanical engineering refers to the vibration of a system that is subjected to an external force or excitation. It occurs when an external force is applied to a vibrating system at a frequency that is different from its natural frequency. This can lead to resonance, where the amplitude of vibration increases significantly.
2. How is forced vibration different from free vibration?
Ans. Forced vibration is different from free vibration in that it is caused by an external force or excitation, whereas free vibration occurs when a system vibrates without any external force acting upon it. Free vibration is dependent on the natural frequency of the system, while forced vibration is influenced by the frequency and magnitude of the external force.
3. What are the applications of forced vibration in mechanical engineering?
Ans. Forced vibration has various applications in mechanical engineering. It is commonly used in the design and analysis of structures to determine their response to external forces, such as earthquakes, wind loads, or machinery vibrations. Forced vibration analysis is also crucial in the design of vehicles, aircraft, and rotating machinery to ensure their stability and performance.
4. How does resonance occur in forced vibration?
Ans. Resonance occurs in forced vibration when the frequency of the external force matches or is close to the natural frequency of the vibrating system. In this condition, the amplitude of vibration increases significantly, potentially leading to excessive stress and damage. Resonance can occur in various mechanical systems, such as bridges, buildings, and rotating machinery.
5. How can forced vibration be controlled or mitigated in mechanical engineering?
Ans. Forced vibration can be controlled or mitigated in mechanical engineering through various methods. One approach is to modify the natural frequency of the system by adjusting its stiffness or mass properties. Damping techniques, such as the use of viscoelastic materials or tuned mass dampers, can also be employed to dissipate the energy and reduce the amplitude of vibration. Additionally, careful design and analysis can help avoid resonance conditions by ensuring that the system's natural frequency is sufficiently different from the expected excitation frequencies.
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Document Description: GATE Past Year Questions: Forced Vibration for Mechanical Engineering 2024 is part of Theory of Machines (TOM) preparation. The notes and questions for GATE Past Year Questions: Forced Vibration have been prepared according to the Mechanical Engineering exam syllabus. Information about GATE Past Year Questions: Forced Vibration covers topics like and GATE Past Year Questions: Forced Vibration Example, for Mechanical Engineering 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for GATE Past Year Questions: Forced Vibration.
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