GATE ME
Theory of Machines
Vibrations
Previous Years Questions

## Marks 1

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 ...
The damping ratio for a viscously damped spring mass system, governed by the relationship $$\,m{{{d^2}x} \over {d{t^2}}} + c{{dx} \over {dt}} + kx = f... The static deflection of a spring under gravity, when a mass of 1 kg is suspended from it, is 1 mm. Assume the acceleration due to gravity g =10 m/s2 ... A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excited by a sinusoidal force of am... Which of the following statements are TRUE for damped vibrations?$$P.$$For a system having critical damping, the value of damping ratio is unity and... In a spring-mass system the mass is m and the spring constant is$$k$$. The critical damping coefficient of the system is$$0.1$$kg/s. In another spr... A point mass is executing simple harmonic motion with an amplitude of$$10$$mm and frequency of$$4$$Hz. The maximum acceleration (m/s2) of the mass... Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displace... Critical damping is the In vibration isolation, which one of the following statements is NOT correct regarding Transmissibility ($$T$$)? If two nodes are observed at a frequency of$$1800$$rpm during whirling of a simply supported long slender rotating shaft, the first critical speed o... The natural frequency of a spring-mass system on earth is$${\omega _n}.$$The natural frequency of this system on the moon (gmoon = gearth/6) is ... The rotor shaft of a large electric motor supported between short bearings at both the ends shows a deflection of$$1.8$$mm in the middle of the roto... For an under damped harmonic oscillator, resonance The differential equation governing the vibrating system is ... There are four samples P, Q, R and S, with natural frequencies 64, 96, 128 and 256 Hz, respectively. There are mounted on test setups for conducting v... A vibrating machine is isolated from the floor using springs. If the ratio of excitation frequency of vibration of machine to the natural frequency of... In the figure shown, the spring deflects by$$\delta $$to position A ( the equilibrium position) when a mass$$m$$is kept on it. During free vibrat... ## Marks 2 The radius of gyration of a compound pendulum about the point of suspension is$$100$$mm. The distance between the point of suspension and the centre... A thin uniform rigid bar of length$$L$$and mass$$M$$is hinged at point$$O,$$located at a distance of$${L \over 3}$$from one of its ends. The b... A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of$$\sqrt {{{3k} \o...
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...
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...
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...
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...
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 ...
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...
Considering massless rigid rod and small oscillations, the natural frequency (in rad/s) of vibration of the system shown in the figure is ...
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...
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 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...
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...
Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length $$0.01m$$. The frequency of vibration of the beam, with...
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 ...
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...
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...
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...
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...
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 $$50$$...
An automotive engine weighing $$240$$ kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of \$...
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 ...
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...
The natural frequency of the spring mass system shown in the figure is closest to ...
The equation of motion of a harmonic oscillator is given by $${{{d^2}x} \over {d{t^2}}} + 2\xi {\omega _n}{{dx} \over {dt}} + \omega _n^2\,x = 0\,\,\,... The natural frequency of the system shown below is ... A machine of$$250$$kg mass is supported on springs of total stiffness$$100$$kN/m. Machine has an unbalanced rotating force of$$350$$N at speed o... A vibratory system consists of a mass$$12.5$$kg, a spring of stiffness$$1000N/m,$$and a dashpot with damping coefficient of$$15Ns/m.$$... A vibratory system consists of a mass$$12.5$$kg, a spring of stiffness$$1000N/m,$$and a dashpot with damping coefficient of$$15Ns/m.$$... In a spring-mass system, the mass is 0.1 kg and the stiffness of the spring is 1 kN/m. By introducing a damper, the frequency of oscillation is found ... A uniform stiff rod of length$$300mm$$and having a weight of$$300N$$is pivoted at one end and connected to a spring at the other end. Fo... A mass M, of 20 kg is attached to the free end of a steel cantilever beam of length 1000 mm having a cross-section of 25$$\, \times \,$$25 mm. Assum... A flexible rotor-shaft system comprises of a$$10kg$$rotor disc placed in the middle of a mass-less shaft of diameter$$30mm$$and length$$500m...
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 ...
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 ...
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...
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 ...
Consider the system of two wagons shown in Figure. The natural frequencies of this system are ...
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

A spring mass $$-$$ dashpot system is shown in the figure. The spring stiffness is $$K,$$ mas is $$m$$, and the viscous damping coefficient is $$c$$. ...
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...
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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