1
GATE ME 2022 Set 1
Numerical
+1
-0

A rigid uniform annular disc is pivoted on a knife edge A in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in the plane of the figure without slip at the pivot point. The inner radius r and outer radius 𝑅 are such that r2 = R2/2, and the acceleration due to gravity is g. If the time period of small amplitude simple harmonic motion is given by $T = β π \sqrt{R/g} $ where π is the ratio of circumference to diameter of a circle, then β = ________ (round off to 2 decimal places).

GATE ME 2022 Set 1 Theory of Machines - Vibrations Question 5 English
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2
GATE ME 2017 Set 2
MCQ (Single Correct Answer)
+1
-0.3
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 freedom system is GATE ME 2017 Set 2 Theory of Machines - Vibrations Question 51 English
A
$$\sqrt {{{2k} \over m}} $$
B
$$\sqrt {{{k} \over m}} $$
C
$$\sqrt {{{k} \over 2m}} $$
D
$$\sqrt {{{4k} \over m}} $$
3
GATE ME 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
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 given by
A
$$\sqrt {{c \over {mk}}} $$
B
$${c \over {2\sqrt {km} }}$$
C
$${c \over {\sqrt {km} }}$$
D
$$\sqrt {{c \over {2mk}}} $$
4
GATE ME 2016 Set 3
Numerical
+1
-0
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 . The natural frequency of this spring-mass system (in rad/s) is _____________
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