GATE ME

Vibrations

Theory of Machines

(Past Years Questions)

Marks 1

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A mass $$m$$ is attached to two identical springs having spring constant $$k$$ as shown in the figure. The natural frequ...
GATE ME 2017 Set 2
The damping ratio for a viscously damped spring mass system, governed by the relationship $$\,m{{{d^2}x} \over {d{t^2}}}...
GATE ME 2017 Set 1
The static deflection of a spring under gravity, when a mass of 1 kg is suspended from it, is 1 mm. Assume the accelerat...
GATE ME 2016 Set 3
A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excit...
GATE ME 2016 Set 1
Which of the following statements are TRUE for damped vibrations? $$P.$$ For a system having critical damping, the value...
GATE ME 2015 Set 3
In a spring-mass system the mass is m and the spring constant is $$k$$. The critical damping coefficient of the system i...
GATE ME 2015 Set 2
A point mass is executing simple harmonic motion with an amplitude of $$10$$ mm and frequency of $$4$$ Hz. The maximum a...
GATE ME 2014 Set 4
Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase ang...
GATE ME 2014 Set 3
Critical damping is the
GATE ME 2014
In vibration isolation, which one of the following statements is NOT correct regarding Transmissibility ($$T$$)?
GATE ME 2014
If two nodes are observed at a frequency of $$1800$$ rpm during whirling of a simply supported long slender rotating sha...
GATE ME 2013
The natural frequency of a spring-mass system on earth is $${\omega _n}.$$ The natural frequency of this system on the m...
GATE ME 2010
The rotor shaft of a large electric motor supported between short bearings at both the ends shows a deflection of $$1.8$...
GATE ME 2009
For an under damped harmonic oscillator, resonance
GATE ME 2007
The differential equation governing the vibrating system is ...
GATE ME 2006
There are four samples P, Q, R and S, with natural frequencies 64, 96, 128 and 256 Hz, respectively. There are mounted o...
GATE ME 2005
A vibrating machine is isolated from the floor using springs. If the ratio of excitation frequency of vibration of machi...
GATE ME 2004
In the figure shown, the spring deflects by $$\delta $$ to position A ( the equilibrium position) when a mass $$m$$ is ...
GATE ME 2001

Marks 2

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The radius of gyration of a compound pendulum about the point of suspension is $$100$$ mm. The distance between the poin...
GATE ME 2017 Set 2
A thin uniform rigid bar of length $$L$$ and mass $$M$$ is hinged at point $$O,$$ located at a distance of $${L \over 3}...
GATE ME 2017 Set 1
A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation ...
GATE ME 2016 Set 3
The system shown in the figure consists of block A of mass 5 kg connected to a spring through a massless rope passing ov...
GATE ME 2016 Set 2
A solid disc with radius a is connected to a spring at a point $$d$$ above the center of the disc. The other end of the...
GATE ME 2016 Set 1
Figure shows a single degree of freedom system. The system consists of a mass less rigid bar $$OP$$ hinged at $$O$$ and ...
GATE ME 2015 Set 3
A single-degree-freedom spring mass system is subjected to a sinusoidal force of $$10$$ N amplitude and frequency $$\ome...
GATE ME 2015 Set 2
Considering massless rigid rod and small oscillations, the natural frequency (in rad/s) of vibration of the system shown...
GATE ME 2015 Set 1
A mobile phone has a small motor with an eccentric mass used for vibrator mode. The location of the eccentric mass on mo...
GATE ME 2015 Set 1
A precision instrument package (m = 1kg) needs to be mounted on a surface vibrating at 60 Hz. It is desired that only 5%...
GATE ME 2015 Set 1
A single degree of freedom system has a mass of 2kg, stiffness 8 N/m and viscous damping ratio 0.02. The dynamic magnifi...
GATE ME 2014 Set 4
The damping ratio of a single degree of freedom spring-mass-damper system with mass of $$1$$ kg, stiffness $$100 N/m$$ a...
GATE ME 2014 Set 3
A mass-spring-dashpot system with mass m = 10 kg, spring constant k = 6250 N/m is excited by a harmonic excitation of 10...
GATE ME 2014 Set 3
What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plan...
GATE ME 2014 Set 2
Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length $$0.01m$$. The frequency ...
GATE ME 2014 Set 1
A rigid uniform rod $$AB$$ of length $$L$$ and mass $$m$$ is hinged at $$C$$ such that $$AC = L/3, CB = 2L/3.$$ Ends $$A...
GATE ME 2014 Set 1
A single degree of freedom system having mass $$1$$ $$kg$$ and stiffness $$10$$ $$kN/m$$ initially at rest is subjected ...
GATE ME 2013
A concentrated mass $$m$$ is attached at the centre of a rod of length $$2L$$ as shown in the figure. The rod is kept in...
GATE ME 2012
A disc of mass m is attached to a spring of stiffness $$k$$ as shown in the figure. The disc rolls without slipping on...
GATE ME 2011
A mass of $$1$$ kg is attached to two identical springs each with stiffness $$k=20kN/m$$ as shown in the figure. Under f...
GATE ME 2011
A mass $$m$$ attached to a spring is subjected to a harmonic force as shown in the figure. The amplitude of the forced m...
GATE ME 2010
An automotive engine weighing $$240$$ kg is supported on four springs with linear characteristics. Each of the front two...
GATE ME 2009
A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is $$3.6$$ kN/m and the damp...
GATE ME 2009
A uniform rigid rod of mass $$m =1kg$$ and length $$L=1$$ m is hinged at its centre & laterally supported at one end b...
GATE ME 2008
The natural frequency of the spring mass system shown in the figure is closest to ...
GATE ME 2008
The equation of motion of a harmonic oscillator is given by $${{{d^2}x} \over {d{t^2}}} + 2\xi {\omega _n}{{dx} \over {d...
GATE ME 2007
The natural frequency of the system shown below is ...
GATE ME 2007
A machine of $$250$$ kg mass is supported on springs of total stiffness $$100$$ kN/m. Machine has an unbalanced rotating...
GATE ME 2006
A vibratory system consists of a mass $$12.5$$ kg, a spring of stiffness $$1000$$ $$N/m,$$ and a dashpot with damping co...
GATE ME 2006
A vibratory system consists of a mass $$12.5$$ kg, a spring of stiffness $$1000$$ $$N/m,$$ and a dashpot with damping co...
GATE ME 2006
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 freq...
GATE ME 2005
A uniform stiff rod of length $$300$$ $$mm$$ and having a weight of $$300$$ $$N$$ is pivoted at one end and connected to...
GATE ME 2004
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...
GATE ME 2004
A flexible rotor-shaft system comprises of a $$10kg$$ rotor disc placed in the middle of a mass-less shaft of diameter $...
GATE ME 2003
A uniform rigid slender bar of mass $$10$$ $$kg.$$ is hinged at the left end is suspended with the help of spring and d...
GATE ME 2003
A uniform rigid slender bar of mass $$10$$ $$kg.$$ is hinged at the left end is suspended with the help of spring and d...
GATE ME 2003
The assembly shown in the figure is composed of two massless rods of length $$l$$ with two particles, each of mass $$m$$...
GATE ME 2001
As shown in Figure, a mass of 100 kg is held between two springs. The natural frequency of vibration of the system, in ...
GATE ME 2000
Consider the system of two wagons shown in Figure. The natural frequencies of this system are ...
GATE ME 1999
A mass of $$1$$ kg is suspended by means of $$3$$ springs as shown in Figure. The spring constants $$\,{K_1},\,{K_2}\,\,...
GATE ME 1996

Marks 5

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A spring mass $$-$$ dashpot system is shown in the figure. The spring stiffness is $$K,$$ mas is $$m$$, and the viscous ...
GATE ME 2001
The suspension system of a two-wheeler can be equated to a single spring-mass system with a viscous damper connected in ...
GATE ME 1997
A cylinder of mass 1 kg and radius 1 m is connected by two identical springs at a height of $$0.5m$$ above the center as...
GATE ME 1996

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