1
GATE ME 2022 Set 1
MCQ (Single Correct Answer)
+2
-0.66
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 ωn are the damping ratio and undamped natural frequency of the system, respectively, while ω is the forcing frequency. The amplitude of the forced steady state response of this system is given by [(1 − r2)2 + (2ζr)2]-1/2, where 𝑟 = ω/ωn. The peak amplitude of this response occurs at a frequency  ω =  ωp. If  ωd denotes the damped natural frequency of this system, which one of the following options is true?
A
ωp < ωd < ωn
B
ωp = ωd < ωn
C
ωd < ωn = ωp
D
ωd < ωn < ωp
2
GATE ME 2017 Set 2
Numerical
+2
-0
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. Considering the acceleration due to gravity as $$9.81$$ m/s2, the natural frequency (in radian/s) of the compound pendulum is _________.
Your input ____
3
GATE ME 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
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 bar is further supported using springs, each of stiffness $$k,$$ located at the two ends. A particle of mass $$m = {m \over 4}$$ is fixed at one end of the bar, as shown in the figure. For small rotations of the bar about $$O,$$ the natural frequency of the systems is GATE ME 2017 Set 1 Theory of Machines - Vibrations Question 15 English
A
$$\sqrt {{{5k} \over {M}}} $$
B
$$\sqrt {{{5k} \over {2M}}} $$
C
$$\sqrt {{{3k} \over {2M}}} $$
D
$$\sqrt {{{3k} \over {M}}} $$
4
GATE ME 2016 Set 3
Numerical
+2
-0
A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of $$\sqrt {{{3k} \over m}} ,$$ the ratio of the amplitude of steady state response to the static deflection of the spring is __________ GATE ME 2016 Set 3 Theory of Machines - Vibrations Question 17 English
Your input ____
GATE ME Subjects
Turbo Machinery
EXAM MAP