1
GATE ME 2023
Numerical
+1
-0

The figure shows a block of mass m = 20 kg attached to a pair of identical linear springs, each having a spring constant k = 1000 N/m. The block oscillates on a frictionless horizontal surface. Assuming free vibrations, the time taken by the block to complete ten oscillations is _________ seconds. (Rounded off to two decimal places)

Take π = 3.14.

GATE ME 2023 Theory of Machines - Vibrations Question 1 English
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2
GATE ME 2022 Set 2
Numerical
+1
-0

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 of this system is measured during a hammer test. A displacement peak in the positive displacement direction is measured to be 4 mm. Neglecting higher powers (> 1) of the damping ratio, the displacement at the next peak in the positive direction will be _______ mm (in integer).

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3
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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4
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
$$\sqrt {{{4k} \over m}} $$
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