1
GATE ME 2016 Set 1
+2
-0.6
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 vertical wall. The disc is free to roll without slipping on the ground. The mass of the disc is $$M$$ and the spring constant is $$K$$. The polar moment of inertia for the disc about its centre is $$J = {{M{a^2}} \over 2}$$ The natural frequency of this system in rad/s is given by

A
$$\sqrt {{{2K{{\left( {a + d} \right)}^2}} \over {3M{a^2}}}}$$
B
$$\sqrt {{{2K} \over {3M}}}$$
C
$$\sqrt {{{2K{{\left( {a + d} \right)}^2}} \over {M{a^2}}}}$$
D
$$\sqrt {{{K{{\left( {a + d} \right)}^2}} \over {M{a^2}}}}$$
2
GATE ME 2015 Set 3
+2
-0.6
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 natural frequency of vibration of the system is A
$${f_n} = {1 \over {2\pi }}\sqrt {{k \over {4m}}}$$
B
$${f_n} = {1 \over {2\pi }}\sqrt {{k \over {2m}}}$$
C
$${f_n} = {1 \over {2\pi }}\sqrt {{k \over {m}}}$$
D
$${f_n} = {1 \over {2\pi }}\sqrt {{{2k} \over m}}$$
3
GATE ME 2015 Set 2
+2
-0.6
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 spring is $$150$$N/m, damping factor is $$0.2$$ and the undamped natural frequency is $$10$$$$\omega$$. At steady state, the amplitude of vibration (in m) is approximately
A
$$0.05$$
B
$$0.07$$
C
$$0.70$$
D
$$0.90$$
4
GATE ME 2015 Set 1
+2
-0.6
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 gravity $$(CG)$$ of the mobile and the rest of the dimensions of the mobile phone are shown. The mobile is kept on a flat horizontal surface. Given in addition that the eccentric mass = $$2$$ grams, eccentricity = $$2.19$$ mm, mass of the mobile = $$90$$ grams, g = $$9.81$$ $$m/{s^2}.$$ Uniform speed of the motor in $$RPM$$ for which the mobile will get just lifted off the ground at the end $$Q$$ is approximately

A
$$3000$$
B
$$3500$$
C
$$4000$$
D
$$4500$$
GATE ME Subjects
Engineering Mechanics
Strength of Materials
Theory of Machines
Engineering Mathematics
Machine Design
Fluid Mechanics
Turbo Machinery
Heat Transfer
Thermodynamics
Production Engineering
Industrial Engineering
General Aptitude
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