What type of damping force is proportional to the displacement of the system?
a) Viscous damping b) Coulomb damping c) Hysteresis damping d) Structural damping
The correct answer and explanation is:
The correct answer is a) Viscous damping.
Viscous damping is a type of damping force that is directly proportional to the velocity of the system, not displacement. However, the question might be referring to how the damping force behaves in relation to the displacement of the system in a general sense.
In systems experiencing viscous damping, the damping force acts in the opposite direction to the velocity of the moving part, and it resists the motion by dissipating energy. The mathematical model of viscous damping involves a force that is proportional to the velocity. The equation for viscous damping can be written as: Fdamping=−cvF_{\text{damping}} = -c v
where:
- FdampingF_{\text{damping}} is the damping force.
- cc is the damping coefficient.
- vv is the velocity of the object.
While this force depends on velocity, the velocity itself is related to the displacement of the system. For instance, in simple harmonic motion, velocity is the time derivative of displacement. Therefore, viscous damping can influence the displacement over time by opposing the motion and gradually reducing the system’s amplitude.
In contrast:
- Coulomb damping involves a constant frictional force, which is independent of velocity or displacement. It usually represents dry friction, which results in a constant resistive force.
- Hysteresis damping is associated with energy dissipation due to internal friction within materials when they undergo cyclic loading. This force is related to the history of the material’s deformation, not just its displacement or velocity.
- Structural damping represents energy loss due to the internal friction within the structure itself, which might be affected by the material properties and construction, but it does not have a simple proportional relationship to displacement.
In summary, viscous damping is primarily defined by its dependence on velocity, which in turn is tied to displacement. However, it remains the closest answer to the concept of a damping force that relates to displacement in terms of its overall effects on motion.