Which of the following describes a characteristic of overdamped systems?

Which of the following describes a characteristic of overdamped systems?

• A. Exhibits oscillatory motion
• B. Exhibits slow return to equilibrium
• C. Reaches equilibrium quickly
• D. Has a damping ratio equal to zero

Answer: (B)

An overdamped system is characterized by its response to disturbances, particularly in how it returns to equilibrium. In this context, the defining feature of an overdamped system is that it exhibits a slow return to equilibrium. This occurs because the damping force is sufficiently high, which suppresses oscillations and prolongs the time it takes for the system to settle back to its equilibrium position. In contrast, oscillatory motion is typically associated with underdamped systems, which can oscillate as they approach equilibrium. A system that reaches equilibrium quickly would likely be critically damped or underdamped, as these types do not exhibit the prolonged settling times that characterize an overdamped response. Lastly, a damping ratio of zero indicates no damping at all and does not describe an overdamped system, as overdamping requires a positive but high damping ratio to achieve the effects described. Thus, the slow return to equilibrium is the standout characteristic that accurately describes overdamped systems.

An overdamped system is characterized by its response to disturbances, particularly in how it returns to equilibrium. In this context, the defining feature of an overdamped system is that it exhibits a slow return to equilibrium. This occurs because the damping force is sufficiently high, which suppresses oscillations and prolongs the time it takes for the system to settle back to its equilibrium position.

In contrast, oscillatory motion is typically associated with underdamped systems, which can oscillate as they approach equilibrium. A system that reaches equilibrium quickly would likely be critically damped or underdamped, as these types do not exhibit the prolonged settling times that characterize an overdamped response. Lastly, a damping ratio of zero indicates no damping at all and does not describe an overdamped system, as overdamping requires a positive but high damping ratio to achieve the effects described. Thus, the slow return to equilibrium is the standout characteristic that accurately describes overdamped systems.