GATE Prev Year : Vibrations Test-7

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Question 1

Rayleigh-Ritz equation determines:

• ACritical speed of shaft
• BCritical speed of machine
• CCritical speed of oscillation
• DNone of these

Question 2

Which of the following statements axe TRUE for damped vibrations?
P. For a system having critical damping, the value of damping ratio is unity and system does not undergo a vibratory motion
Q. Logarithmic decrement method is used to determine the amount of damping in a physical system.
R. In case of damping due to dry friction between moving surfaces resisting force of constant magnitude acts opposite to the relative motion.
S. For the case of viscous damping, drag force is directly proportional to the square of relative velocity:

• AP and Q only
• BP and S only
• CP, Q and R only
• DQ and S only

Question 3

A uniform rigid slenderbar of mass 10 kg, hinged at the left end is suspended with the help of spring and damper arrangement as shown in the figure where K = 2kN/m, C =500 Ns/m and the stiffness of the torsional spring K_θ is 1 kN/m/rad. Ignore the hinge dimensions.

The un-damped natural frequency of oscillations of the bar about the hinge point is

• A 42.43 rad/s
• B 30 rad/s
• C 17.32 rad/s
• D 14.14 rad/s

Question 4

A uniform rigid slenderbar of mass 10 kg, hinged at the left end is suspended with the help of spring and damper arrangement as shown in the figure where K = 2kN/m, C =500 Ns/m and the stiffness of the torsional spring K_θ is 1 kN/m/rad. Ignore the hinge dimensions.

The damping coefficient in the vibration equation is given by

• A 500 Nms/rad
• B 500 N/(m/s)
• C 80 Nms/rad
• D 80 N/(m/s)

Question 5

What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by m and the spring constants are denoted by and as shown below.

• A
• B
• C
• D

Question 6

A mass m is attached at centre of rod having length 2b. The rod is in horizontal position through a spring having stiffness a. If we neglect the weight of rod and spring, then the undamped natural frequency of particular system will be:

• A√a/m
• B√2a/m
• C√a/2m
• D√4a/m

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