1
GATE ME 2024
Numerical
+2
-1.33

A vibratory system consists of mass $m$, a vertical spring of stiffness $2k$ and a horizontal spring of stiffness $k$. The end $A$ of the horizontal spring is given a horizontal motion $x_A = a \sin \omega t$. The other end of the spring is connected to an inextensible rope that passes over two massless pulleys as shown.

Assume $m = 10 kg$, $k = 1.5$ kN/m, and neglect friction.

The magnitude of critical driving frequency for which the oscillations of mass $m$ tend to become excessively large is _____ rad/s (answer in integer).

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 _________.
3
GATE ME 2017 Set 1
+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
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 __________