GATE Mechanical Engineering

A block of mass 1 kg connected to a spring of stiffness $10 \mathrm{~N} \mathrm{~m}^{-1}$ is operating in a viscous medium such that the damping ratio (or damping factor) is equal...

In the context of balancing of rotating and reciprocating masses, which one of the following options is true?

A linear spring-mass-dashpot system with a mass of 2 kg is set in motion with viscous damping. If the natural frequency is 15 Hz, and the amplitudes of two successive cycles measur...

The change in kinetic energy $\Delta E$ of an engine is $300$ J, and minimum and maximum shaft speeds are $\omega_{min} = 220$ rad/s and $\omega_{max} = 280$ rad/s, respectively. A...

Consider a forced single degree-of-freedom system governed by $\rm \ddot x(t) + 2 ζ ω_n \dot x (t) + ω_n^2 x(t) = ω_n^2 \cos (ω t)$ , where ζ and ω n are the damping ratio and unda...

For a dynamical system governed by the equation, $\ddot{x}(t)+2 ζ \omega_n \dot{x}(t)+\omega_n^2x(t)=0$ the damping ratio ζ is equal to $\frac{1}{2\pi}\log_e2$ . The displacement x...

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 of mass is $$250$$ mm. Consid...

The damping ratio for a viscously damped spring mass system, governed by the relationship $$\,m{{{d^2}x} \over {d{t^2}}} + c{{dx} \over {dt}} + kx = f\left( t \right),\,\,\,$$ is g...

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/s 2 . The natural frequency of th...

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 amplitude 100 N. If the damping...

The number of degrees of freedom in a planner mechanism having $$n$$ links and $$j$$ simple hinge joints is

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 spring mass system, the mass is $...

The torque (in N-m) exerted on the crank shaft of a two stroke engine can be described as is the crank angle as $$\,\,T = 10000 + 1000\sin 2\theta - 1200\,\cos 2\theta ,\,\,$$ wher...

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 vib...

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 amplitude be transmitted to t...

In a certain slider-crank mechanism, lengths of crank and connecting rod are equal. If the crank rotates with a uniform angular speed of 14 rad/s and the crank length is 300 mm, th...

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 spring. The stiffness of the spr...

It is desired to avoid interference in a pair of spur gears having a 20 o pressure angle. With increase in pinion to gear speed ratio, the minimum number of teeth on the pinion

A circular object of radius r rolls without $$V$$ slipping on a horizontal level floor with the center having velocity $$V.$$ The velocity at the point of contact between the objec...

A point mass is executing simple harmonic motion with an amplitude of $$10$$ mm and frequency of $$4$$ Hz. The maximum acceleration (m/s 2 ) of the mass is _________.

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 of $$25$$ $$N.s/m$$ is ______...

Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length $$0.01m$$. The frequency of vibration of the beam, with a $$0.5$$ kg mass attached at...

Critical damping is the

Which one of the following is used to convert a rotational motion into a translational motion?

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 excit...

Maximum fluctuation of kinetic energy in an engine has been calculated to be $$2600$$ J. Assuming that the engine runs at an average speed of $$200$$ rpm, the polar mass moment of...

In vibration isolation, which one of the following statements is NOT correct regarding Transmissibility ($$T$$)?

For the given statements: ($$I.$$) $$\,\,\,$$ Mating spur gear teeth is an example of higher pair ($$II.$$) $$\,\,\,$$ A revolute joint is an example of lower pair. Indicate the co...

Consider a flywheel whose mass $$M$$ is distributed almost equally between a heavy, ring-like rim of radius $$R$$ and a concentric disk-like feature of radius $$R/2$$. Other parts...

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 frequency of 1.5 rad/s is ___...

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 of the shaft in rpm is

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 magnitude $$5$$ $$kN$$ for $${10^{ -...

A flywheel connected to a punching machine has to supply energy of $$400$$ Nm while running at a mean angular speed of $$20$$ rad/s. If the total fluctuation of speed is not to exc...

The following are the data for two crossed helical gears used for speed reduction: Gear $$I:$$ Pitch circle diameter in the plane of rotation 80mm and helix angle 30 o Gear $$II:$$...

A circular solid disc of uniform thickness $$20mm,$$ radius $$200mm$$ and $$mass$$ $$20kg,$$ is used as a fly wheel. If it rotates at $$600$$ $$rpm,$$ the kinetic energy of the fly...

Mobility of a statically indeterminate structure is

Tooth interference in an external involute spur gear pair can be reduced by

There are two points P and Q on a planar rigid body. The relative velocity between the two points

Which of the following statements is INCORRECT

The natural frequency of a spring-mass system on earth is $${\omega _n}.$$ The natural frequency of this system on the moon (g moon = g earth /6) is

Match the approaches given below to perform stated kinematics/dynamics analysis of machine Analysis $$P.$$ Continuous relative rotation $$Q.$$ Velocity and acceleration $$R.$$ Mobi...

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...

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 rotor. Assuming the rotor to be pe...

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 $$...

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 constant $$k=300N/m.$$ The natural freque...

A planar mechanism has 8 links and 10 rotary joints. The number of degrees of freedom of the mechanism, using Gruebler's criterion, is

For an under damped harmonic oscillator, resonance

The speed of an engine varies from $$210$$ rad/s to $$190$$ rad/s. During cycle the change in kinetic energy is found to be $$400$$ Nm. The inertia of the flywheel in kgm 2 is

The equation of motion of a harmonic oscillator is given by $${{{d^2}x} \over {d{t^2}}} + 2\xi {\omega _n}{{dx} \over {dt}} + \omega _n^2\,x = 0\,\,\,$$ and the initial conditions...

If $${C_f}$$ is the coefficient of speed fluctuation of a flywheel then the ratio of $${\omega _{\max }}/{\omega _{\min }}$$ will be

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 of $$3600$$ rpm. Assuming a dam...

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...

In a four-bar linkage, $$S$$ denotes the shortest link length, $$L$$ is the longest link length, $$P$$ and $$Q$$ are the lengths of other two links. At least one of the three movin...

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 logarithmic decre...

For a four bar linkage in Toggle position, the value of mechanical advantage is

Match the items in columns $$I$$ and $$II$$ Column $$I$$ $$P.$$ Addendum $$Q.$$ Instantaneous center of velocity $$R.$$ Section modulus $$S.$$ Prince circle Column $$II$$ $$1.$$ Ca...

The number of inversions for a slider crank mechanism 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 vibration experiments. If a lou...

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 valu...

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 the isolation system is equal...

Match the following with respect to spatial mechanism. Type of Joint $$P.$$ Revolute $$Q.$$ Cylindrical $$R.$$ Spherical Motion constrained $$1.$$ Three $$2.$$ Five $$3.$$ Four $$4...

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 $$500mm$$ between bearings (shaft is...

For a certain engine having an average speed of $$1200$$ rpm, a flywheel approximated as a solid disc, is required for keeping the fluctuation of speed within $$2$$% about the aver...

The overall gear ratio in a 2 stage speed reduction gear box (with all spur gears) is 12. The input and output shafts of the gear box are collinear. The countershafts which is para...

The lengths of the links of a 4-bar linkage with revolute pairs only are $$p,q,r$$ and $$s$$ units. Given that $$p < q < r < s.$$ Which of these links should be the fixed one, for...

The overall gear ratio in a 2 stage speed reduction gear box (with all spur gears) is 12. The input and output shafts of the gear box are collinear. The countershafts which is para...

The mechanism used in a shaping machine is

Which of the following statement is correct?

A 1.5 kW motor is running at 1440 rev/min. Its is to be connected to a stirrer running at 36 rev/min. The gearing arrangement suitable for this application is

A flywheel of moment of inertia $$9.8$$ kg m 2 fluctuates by $$30$$ rpm for a fluctuation in energy of $$1936$$ Jouls. The mean speed of the flywheel is (in rpm)

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 diagram and give the equations...

List $$I$$ (Gear types) (a) Worm gears (b) Cross helical gears (c) Bevel gears (d) Spur gears List $$II$$ (Applications) 1. Parallel shafts 2. Non-parallel, intersecting shafts 3....

In spur gears having involute teeth, the product of circular pitch and diametral pitch is _________

Instantaneous center of a body rolling with sliding on a stationary curved surface lies