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GATE 2020: Theory of Machine Quiz 8

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Question 1

Which statement regarding damping is correct?

Question 2

The damping ratio of a single degree of freedom spring-mass-damper system with mass of 1 kg, stiffness 400 N/m and viscous damping coefficient of 25 N.s/m is ______

Question 3

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:

Question 4

A concentrated mass m is attached at the centre of a rod of length 2L as shown in the figure. The rod is kept in a horizontal equilibrium position by a spring of stiffness k. For very small amplitude of vibration, neglecting the weights of the rod and spring, the undamped natural frequency of the system is

Question 5

A weighing machine consists of 2 kg pan resting on a spring. At this condition, the length of spring is 200 mm. When a 20 kg mass is placed on the pan, the length of spring becomes 100 mm. The undeformed length L in mm and spring stiffness k in N/m are

Question 6

A rigid uniform rod AB of length L and mass m is hinged at C such that AC= L/3, CB = 2L/3. Ends A and B are supported by springs of spring constant k. The natural frequency of the system is given by

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ESE & GATE ME Theory of Machines & Vibrations

May 7ESE & GATE ME