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# Damped Free Vibrations: Viscous damping MCQs

1. What is the coefficient of damping in a damped free vibration system?

a) The ratio of viscous force to velocity
b) The ratio of damping force to displacement
c) The ratio of displacement to velocity
d) The ratio of damping force to velocity

Answer: a) The ratio of viscous force to velocity

Explanation: The coefficient of damping in a damped free vibration system represents the proportionality between the damping force and the velocity of the vibrating system. In viscous damping, this coefficient is typically related to the viscosity of the medium through which the system is moving.

2. What does the damping ratio indicate in a vibrating system?

a) The ratio of energy dissipated to energy stored
b) The ratio of displacement to maximum displacement
c) The ratio of damping force to restoring force
d) The ratio of amplitude to frequency

Answer: a) The ratio of energy dissipated to energy stored

Explanation: The damping ratio quantifies the level of damping in a vibrating system by comparing the energy dissipated due to damping to the energy stored in the system. It is a crucial parameter for characterizing the behavior of damped vibrations.

3. In an underdamped system, the damping ratio is:

a) Less than 1
b) Equal to 1
c) Greater than 1
d) Equal to 0

Answer: a) Less than 1

Explanation: An underdamped system has a damping ratio less than 1, indicating that the damping effect is present but not strong enough to prevent oscillations from occurring. This results in oscillatory behavior with decaying amplitude.

4. What is the logarithmic decrement used for in analyzing damped vibrations?

a) To determine the frequency of vibration
b) To measure the damping ratio
c) To calculate the energy dissipated per cycle
d) To estimate the maximum displacement

Answer: c) To calculate the energy dissipated per cycle

Explanation: The logarithmic decrement is a measure of the rate at which the amplitude of oscillations decreases in a damped vibration system. It is used to calculate the energy dissipated per cycle, providing insight into the damping characteristics of the system.

5. In an overdamped system, the damping ratio is:

a) Less than 1
b) Equal to 1
c) Greater than 1
d) Equal to 0

Answer: c) Greater than 1

Explanation: An overdamped system has a damping ratio greater than 1, indicating that the damping effect is strong enough to prevent oscillations from occurring. Instead, the system returns to its equilibrium position without oscillating.

6. What is the frequency of damped free vibration determined by?

a) Damping coefficient
b) Damping ratio
c) Mass and stiffness of the system
d) Amplitude of vibration

Answer: c) Mass and stiffness of the system

Explanation: The frequency of damped free vibration is primarily determined by the mass and stiffness of the vibrating system. Damping affects the amplitude and decay rate of the vibrations but does not directly determine the frequency.

7. Coulomb or dry friction damping occurs due to:

a) Viscous forces
b) Internal friction within the material
c) Friction between surfaces in contact
d) Electromagnetic forces

Answer: c) Friction between surfaces in contact

Explanation: Coulomb or dry friction damping arises from the frictional forces between surfaces in contact within the vibrating system. Unlike viscous damping, which is related to fluid viscosity, Coulomb damping is associated with solid friction.

8. What is the primary difference between viscous and Coulomb damping?

a) Viscous damping depends on the material properties, while Coulomb damping depends on the surface roughness.
b) Viscous damping occurs in liquids, while Coulomb damping occurs in solids.
c) Viscous damping is proportional to velocity, while Coulomb damping is independent of velocity.
d) Viscous damping dissipates energy continuously, while Coulomb damping dissipates energy only when motion occurs.

Answer: d) Viscous damping dissipates energy continuously, while Coulomb damping dissipates energy only when motion occurs.

Explanation: Viscous damping dissipates energy continuously as the system moves, proportional to the velocity of the motion. In contrast, Coulomb damping only dissipates energy when there is relative motion between surfaces, irrespective of the velocity.

9. What type of damping is associated with slip or interfacial damping?

a) Viscous damping
b) Coulomb damping
c) Solid damping
d) Structural damping

Answer: b) Coulomb damping

Explanation: Slip or interfacial damping involves the sliding or relative motion between surfaces, which generates frictional forces. This type of damping is characteristic of Coulomb damping, where the damping force is directly proportional to the normal force between the surfaces.

10. Which type of damping is primarily related to internal friction within the material?

a) Viscous damping
b) Coulomb damping
c) Solid damping
d) Structural damping

Answer: c) Solid damping

Explanation: Solid damping, also known as material or hysteresis damping, arises from internal friction within the material of the vibrating system. It is distinct from Coulomb damping, which involves friction between surfaces, and viscous damping, which occurs in fluids.