GATE ME 2015 Set 3 — Question 39
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Theory of Machines & Vibrations → Free Vibration → Damped Free Vibration
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Question
Which of the following statements are 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.
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.
Correct answer
(C) P, Q and R only
Solution
P is TRUE: Critical damping occurs when the damping ratio . In this state, the system returns to equilibrium in the shortest time without oscillation.
Q is TRUE: Logarithmic decrement () is a standard method to measure damping in underdamped systems by comparing successive peak amplitudes.
R is TRUE: Coulomb damping (dry friction) is characterized by a constant magnitude force () that always opposes the direction of motion.
S is FALSE: In linear viscous damping, the damping force is directly proportional to the relative velocity (), not the square of the velocity.Thus, P, Q, and R are true statements.
Q is TRUE: Logarithmic decrement () is a standard method to measure damping in underdamped systems by comparing successive peak amplitudes.
R is TRUE: Coulomb damping (dry friction) is characterized by a constant magnitude force () that always opposes the direction of motion.
S is FALSE: In linear viscous damping, the damping force is directly proportional to the relative velocity (), not the square of the velocity.Thus, P, Q, and R are true statements.
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