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

Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:A slender uniform rigid bar of mass mis hinged at O an d supported by two springs, with stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For the system to be critically damped, the ratio c√km should be
GATE Past Year Questions: Damped & Undamped Vibration | Theory of Machines (TOM) - Mechanical Engineering
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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:The natural frequencies corresponding to the spring-mass system I an d II are ωI an d ωII , respectively. The ratio GATE Past Year Questions: Damped & Undamped Vibration | Theory of Machines (TOM) - Mechanical Engineeringis
GATE Past Year Questions: Damped & Undamped Vibration | Theory of Machines (TOM) - Mechanical Engineering
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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:A thin uniform rigid bar of length L and M is hinged at point O, located at a distance of L/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/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 system is
GATE Past Year Questions: Damped & Undamped Vibration | Theory of Machines (TOM) - Mechanical Engineering

[2017]

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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:A mass m is attached to two identical springs having constant k as shown in the figure. The natural frequency w of this single degree of freedom system is
GATE Past Year Questions: Damped & Undamped Vibration | Theory of Machines (TOM) - Mechanical Engineering

[2017]

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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:Considering mass less rigid rod small oscillations, the natural frequency (in rad/s) of vibration of the system shown in the figure is
GATE Past Year Questions: Damped & Undamped Vibration | Theory of Machines (TOM) - Mechanical Engineering

[2015]

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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless.The mass of the block is denoted by m and the spring constants are denoted by k1 and k2 as shown below
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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:A rigid uniform rod AB of length L and mass m is hinged at C such that AC = L/3, CB = 2L/3.
Ends A and B are supported by springs of spring constant k. The natural frequency of the system is given by
GATE Past Year Questions: Damped & Undamped Vibration | Theory of Machines (TOM) - Mechanical Engineering

[2014]

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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:A concentrated mass m is attached at the centre of a rod of Iength 2L as shown in the figure.
The rod is kept in a horizontal equilibrium position by a spring of stiffness k. For very small amplitude of vibration, neglecting the weights of the rod and spring, the undamped natural frequency of the system is
GATE Past Year Questions: Damped & Undamped Vibration | Theory of Machines (TOM) - Mechanical Engineering

[2012]

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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:A disc of mass m is attached to a spring of stiffness k as shown in the fig. The disc rolls without slipping on a horizontal surface. The natural frequency of vibration of the system is

GATE Past Year Questions: Damped & Undamped Vibration | Theory of Machines (TOM) - Mechanical Engineering

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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:The natural frequency of a spring-mass system on earth is wn. The natural frequency of this system on the moon

[2010]

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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:A uniform rigid rod of mass m = 1 kg and length L = 1 m is hinged at its centre & laterally supported at one end by a spring of spring constant k = 300 N/m. The natural frequency wn in rad/s is

[2008]

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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:The natural frequency of the spring mass system shown in the figure is closest to​

[2008 : 2 Marks]

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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself: The natural frequency of the system shown below
GATE Past Year Questions: Damped & Undamped Vibration | Theory of Machines (TOM) - Mechanical Engineering
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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:For an under damped harmonic oscillator, resonance

[2007]

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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:A uniform stiff rod of length 300 mm and having a weight of 300 N is pivoted at one end and connected to a spring at the other end. For keeping the rod vertical in a stable position the minimum value of spring constant K needed is
GATE Past Year Questions: Damped & Undamped Vibration | Theory of Machines (TOM) - Mechanical Engineering

[2004]

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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:The assembly shown in the figure is composed of two massless rods of length l with two particles, each of mass m. The natural frequency of this assembly for small oscillations is
GATE Past Year Questions: Damped & Undamped Vibration | Theory of Machines (TOM) - Mechanical Engineering

[2001]

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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:In the figure shown, the spring deflects by d to position A (the equilibrium position) when a mass m is kept on it. During free vibration, the mass is at position B at some instant. The change in potential energy of the spring mass system from position A to position B is
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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:As shown in figure, a mass of 100 kg is held between two springs. The natural frequency of vibration of the system in cycle/s, is
GATE Past Year Questions: Damped & Undamped Vibration | Theory of Machines (TOM) - Mechanical Engineering

[2000]

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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:Consider the system of two wagons shown in figure. The natural frequencies of this system are

[1999]

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Question for GATE Past Year Questions: Damped & Undamped Vibration
Try yourself:A mass of 1 kg is suspended by means of 3 springs as shown in figure. The spring constant K1, K2 and K3 are respectively 1 kN/m, 3 kN/m and 2 kN/m. The natural frequency of the system is approximately

GATE Past Year Questions: Damped & Undamped Vibration | Theory of Machines (TOM) - Mechanical Engineering

[1996]

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The document GATE Past Year Questions: Damped & Undamped Vibration | Theory of Machines (TOM) - Mechanical Engineering is a part of the Mechanical Engineering Course Theory of Machines (TOM).
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FAQs on GATE Past Year Questions: Damped & Undamped Vibration - Theory of Machines (TOM) - Mechanical Engineering

1. What is damped vibration in mechanical engineering?
Ans. Damped vibration refers to the oscillatory motion of a mechanical system that gradually decreases over time due to the dissipative effects of damping. Damping can be introduced through various means such as friction, fluid resistance, or material properties. The damping force acts opposite to the direction of motion, reducing the amplitude of vibration until the system comes to a rest.
2. How is undamped vibration different from damped vibration?
Ans. Undamped vibration in mechanical engineering refers to the oscillatory motion of a system without any dissipation of energy. Unlike damped vibration, undamped vibration does not experience any reduction in amplitude over time. This type of vibration occurs in ideal systems with no energy losses, such as a mass-spring system without any external resistance or friction.
3. What are the causes of damping in mechanical systems?
Ans. Damping in mechanical systems can be caused by various factors, including frictional forces between moving parts, air resistance, fluid flow resistance, and material properties. Frictional damping occurs when two surfaces slide or rub against each other, converting the kinetic energy of motion into heat. Fluid damping occurs when a fluid medium, such as air or liquid, resists the motion of an object passing through it, dissipating energy in the process.
4. How does damping affect the natural frequency of a vibrating system?
Ans. Damping affects the natural frequency of a vibrating system by reducing it. The presence of damping in a system causes energy dissipation, which leads to a decrease in the amplitude of vibration over time. As a result, the natural frequency of the system decreases, as the system takes longer to complete each oscillation. Damping also introduces a damping factor that affects the overall behavior and response of the system.
5. What are the practical applications of damped and undamped vibrations in mechanical engineering?
Ans. Damped and undamped vibrations find practical applications in various mechanical engineering systems. Undamped vibrations are utilized in precision instruments, such as atomic force microscopes, where minimizing energy loss is crucial for accurate measurements. Damped vibrations, on the other hand, are commonly encountered in vehicles' suspension systems, buildings' earthquake resistance design, or even musical instruments, where controlled damping is desired to enhance performance and reduce undesired vibrations.
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