Vibrations · Theory of Machines · GATE ME

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Marks 1

GATE ME 2017 Set 2
A mass $$m$$ is attached to two identical springs having spring constant $$k$$ as shown in the figure. The natural frequency of this single degree of ...
GATE ME 2017 Set 1
The damping ratio for a viscously damped spring mass system, governed by the relationship $$\,m{{{d^2}x} \over {d{t^2}}} + c{{dx} \over {dt}} + kx = f...
GATE ME 2016 Set 3
The static deflection of a spring under gravity, when a mass of 1 kg is suspended from it, is 1 mm. Assume the acceleration due to gravity g =10 m/s2 ...
GATE ME 2016 Set 1
A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excited by a sinusoidal force of am...
GATE ME 2015 Set 3
Which of the following statements are TRUE for damped vibrations? $$P.$$ For a system having critical damping, the value of damping ratio is unity and...
GATE ME 2015 Set 2
In a spring-mass system the mass is m and the spring constant is $$k$$. The critical damping coefficient of the system is $$0.1$$ kg/s. In another spr...
GATE ME 2014 Set 4
A point mass is executing simple harmonic motion with an amplitude of $$10$$ mm and frequency of $$4$$ Hz. The maximum acceleration (m/s2) of the mass...
GATE ME 2014 Set 3
Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displace...
GATE ME 2014
Critical damping is the
GATE ME 2014
In vibration isolation, which one of the following statements is NOT correct regarding Transmissibility ($$T$$)?
GATE ME 2013
If two nodes are observed at a frequency of $$1800$$ rpm during whirling of a simply supported long slender rotating shaft, the first critical speed o...
GATE ME 2010
The natural frequency of a spring-mass system on earth is $${\omega _n}.$$ The natural frequency of this system on the moon (gmoon = gearth/6) is ...
GATE ME 2009
The rotor shaft of a large electric motor supported between short bearings at both the ends shows a deflection of $$1.8$$ mm in the middle of the roto...
GATE ME 2007
For an under damped harmonic oscillator, resonance
GATE ME 2006
The differential equation governing the vibrating system is ...
GATE ME 2005
There are four samples P, Q, R and S, with natural frequencies 64, 96, 128 and 256 Hz, respectively. There are mounted on test setups for conducting v...
GATE ME 2004
A vibrating machine is isolated from the floor using springs. If the ratio of excitation frequency of vibration of machine to the natural frequency of...
GATE ME 2001
In the figure shown, the spring deflects by $$\delta $$ to position A ( the equilibrium position) when a mass $$m$$ is kept on it. During free vibrat...

Marks 2

GATE ME 2017 Set 2
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...
GATE ME 2017 Set 1
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 b...
GATE ME 2016 Set 3
A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of $$\sqrt {{{3k} \o...
GATE ME 2016 Set 2
The system shown in the figure consists of block A of mass 5 kg connected to a spring through a massless rope passing over pulley B of radius r and ma...
GATE ME 2016 Set 1
A solid disc with radius a is connected to a spring at a point $$d$$ above the center of the disc. The other end of the spring is fixed to the vertic...
GATE ME 2015 Set 3
Figure shows a single degree of freedom system. The system consists of a mass less rigid bar $$OP$$ hinged at $$O$$ and a mass $$m$$ at end $$P.$$ The...
GATE ME 2015 Set 2
A single-degree-freedom spring mass system is subjected to a sinusoidal force of $$10$$ N amplitude and frequency $$\omega $$ along the axis of the sp...
GATE ME 2015 Set 1
A precision instrument package (m = 1kg) needs to be mounted on a surface vibrating at 60 Hz. It is desired that only 5% of the base surface vibration...
GATE ME 2015 Set 1
A mobile phone has a small motor with an eccentric mass used for vibrator mode. The location of the eccentric mass on motor with respect to center of ...
GATE ME 2015 Set 1
Considering massless rigid rod and small oscillations, the natural frequency (in rad/s) of vibration of the system shown in the figure is ...
GATE ME 2014 Set 4
A single degree of freedom system has a mass of 2kg, stiffness 8 N/m and viscous damping ratio 0.02. The dynamic magnification factor at an excitation...
GATE ME 2014 Set 2
What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of...
GATE ME 2014 Set 3
The damping ratio of a single degree of freedom spring-mass-damper system with mass of $$1$$ kg, stiffness $$100 N/m$$ and viscous damping coefficient...
GATE ME 2014 Set 3
A mass-spring-dashpot system with mass m = 10 kg, spring constant k = 6250 N/m is excited by a harmonic excitation of 10 cos(25t) N. At the steady sta...
GATE ME 2014 Set 1
Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length $$0.01m$$. The frequency of vibration of the beam, with...
GATE ME 2014 Set 1
A rigid uniform rod $$AB$$ of length $$L$$ and mass $$m$$ is hinged at $$C$$ such that $$AC = L/3, CB = 2L/3.$$ Ends $$A$$ and $$B$$ are supported by ...
GATE ME 2013
A single degree of freedom system having mass $$1$$ $$kg$$ and stiffness $$10$$ $$kN/m$$ initially at rest is subjected to an impulse force of magnitu...
GATE ME 2012
A concentrated mass $$m$$ is attached at the centre of a rod of length $$2L$$ as shown in the figure. The rod is kept in a horizontal equilibrium posi...
GATE ME 2011
A disc of mass m is attached to a spring of stiffness $$k$$ as shown in the figure. The disc rolls without slipping on a horizontal surface. The natu...
GATE ME 2011
A mass of $$1$$ kg is attached to two identical springs each with stiffness $$k=20kN/m$$ as shown in the figure. Under frictionless condition, the nat...
GATE ME 2010
A mass $$m$$ attached to a spring is subjected to a harmonic force as shown in the figure. The amplitude of the forced motion is observed to be $$50$$...
GATE ME 2009
An automotive engine weighing $$240$$ kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of $...
GATE ME 2009
A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is $$3.6$$ kN/m and the damping constant of the damper is ...
GATE ME 2008
A uniform rigid rod of mass $$m =1kg$$ and length $$L=1$$ m is hinged at its centre & laterally supported at one end by a spring of spring const...
GATE ME 2008
The natural frequency of the spring mass system shown in the figure is closest to ...
GATE ME 2007
The equation of motion of a harmonic oscillator is given by $${{{d^2}x} \over {d{t^2}}} + 2\xi {\omega _n}{{dx} \over {dt}} + \omega _n^2\,x = 0\,\,\,...
GATE ME 2007
The natural frequency of the system shown below is ...
GATE ME 2006
A machine of $$250$$ kg mass is supported on springs of total stiffness $$100$$ kN/m. Machine has an unbalanced rotating force of $$350$$ N at speed o...
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 coefficient of $$15$$ $$Ns/m.$$ ...
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 coefficient of $$15$$ $$Ns/m.$$ ...
GATE ME 2005
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 ...
GATE ME 2004
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. Fo...
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 $$\, \times \,$$ 25 mm. Assum...
GATE ME 2003
A flexible rotor-shaft system comprises of a $$10kg$$ rotor disc placed in the middle of a mass-less shaft of diameter $$30$$ $$mm$$ and length $$500m...
GATE ME 2003
A uniform rigid slender bar of mass $$10$$ $$kg.$$ is hinged at the left end is suspended with the help of spring and damper arrangement as shown in ...
GATE ME 2003
A uniform rigid slender bar of mass $$10$$ $$kg.$$ is hinged at the left end is suspended with the help of spring and damper arrangement as shown in ...
GATE ME 2001
The assembly shown in the figure is composed of two massless rods of length $$l$$ with two particles, each of mass $$m$$. The natural frequency of thi...
GATE ME 2000
As shown in Figure, a mass of 100 kg is held between two springs. The natural frequency of vibration of the system, in cycles/s, is ...
GATE ME 1999
Consider the system of two wagons shown in Figure. The natural frequencies of this system are ...
GATE ME 1996
A mass of $$1$$ kg is suspended by means of $$3$$ springs as shown in Figure. The spring constants $$\,{K_1},\,{K_2}\,\,$$ and $$\,{K_3},$$ are respec...

Marks 5

GATE ME 2001
A spring mass $$-$$ dashpot system is shown in the figure. The spring stiffness is $$K,$$ mas is $$m$$, and the viscous damping coefficient is $$c$$. ...
GATE ME 1997
The suspension system of a two-wheeler can be equated to a single spring-mass system with a viscous damper connected in series. Sketch the free body d...
GATE ME 1996
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 shown in the Fig. The cylinde...
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