Overdempte

Overdempte, or overdamped, is a term used in control theory and mechanics to describe a state of a dynamic system where the damping is stronger than the critical level. This occurs when the damping ratio ζ, a dimensionless measure of damping, is greater than one (ζ > 1). In such cases the system returns to equilibrium without oscillating.

In a standard second-order system with natural frequency ω_n, the typical transfer function is H(s) = ω_n^2 / (s^2 + 2ζω_n s + ω_n^2). For overdamping, the poles are real and negative, located at s = -ω_n(ζ ± √(ζ^2 − 1)). This real-pole structure leads to a non-oscillatory, monotonic approach to the final value when the system is disturbed or subjected to a step input.

The time-domain response of an overdamped system is a sum of two decaying exponentials and shows no overshoot or oscillation. The final value is reached monotonically, but the approach is typically slower than in the critically damped case, with the slower exponential term dominating the tail of the response.

Overdamped configurations appear in various applications, such as mechanical assemblies with heavy damping or weak springs, door closers, certain automotive suspension dampers configured for high damping, and electrical circuits with large resistance in RLC networks. They are contrasted with underdamped systems (ζ < 1), which exhibit oscillations, and critically damped systems (ζ = 1), which achieve the fastest non-oscillatory response. In design, engineers balance damping to avoid excessive sluggishness while preventing overshoot and oscillations.