For critically damped systems, what is true regarding the damping ratio?

For critically damped systems, what is true regarding the damping ratio?

• A. It is less than 1
• B. It is equal to 0
• C. It is equal to 1
• D. It is greater than 1

Answer: (C)

In critically damped systems, the damping ratio is precisely equal to 1. This specific condition means that the system returns to equilibrium as quickly as possible without oscillating. In the context of second-order linear differential equations, the general form of the damping ratio (\(\zeta\)) classifies systems as underdamped (\(\zeta < 1\)), critically damped (\(\zeta = 1\)), or overdamped (\(\zeta > 1\)). For a critically damped system, having a damping ratio of 1 means that the system has just enough damping to prevent oscillations while allowing a return to the equilibrium position in the shortest time possible. Understanding this property is essential in control systems, vibration analysis, and other electrical engineering applications, where controlling the speed of response without overshoot is often a critical design requirement.

In critically damped systems, the damping ratio is precisely equal to 1. This specific condition means that the system returns to equilibrium as quickly as possible without oscillating.

In the context of second-order linear differential equations, the general form of the damping ratio ((\zeta)) classifies systems as underdamped ((\zeta < 1)), critically damped ((\zeta = 1)), or overdamped ((\zeta > 1)). For a critically damped system, having a damping ratio of 1 means that the system has just enough damping to prevent oscillations while allowing a return to the equilibrium position in the shortest time possible.

Understanding this property is essential in control systems, vibration analysis, and other electrical engineering applications, where controlling the speed of response without overshoot is often a critical design requirement.