überdämpft

Überdämpft, in physics and engineering often translated as overdamped, describes a system whose damping is stronger than the critical level. After a disturbance, such a system returns to equilibrium without oscillating, but typically slower than a critically damped one.

In the standard second-order model, a system described by x'' + 2ζωn x' + ωn^2 x = 0 is overdamped when the damping ratio ζ exceeds 1. The solution consists of two exponential terms with decay rates related to −ωn(ζ ± sqrt(ζ^2 − 1)). For a step input, the output moves toward its final value monotonically, without overshoot or ringing.

Overdamping occurs in various contexts. In mechanical systems, high viscous damping (for example via fluids or damping materials) can prevent oscillations of springs or suspensions. In electrical circuits, a large resistance relative to inductance and capacitance can produce overdamped behavior in RLC networks. In control systems, intentional overdamping may be used to avoid overshoot in actuators or safety-critical applications where oscillations are undesirable.

The main trade-off is between speed and stability. While overdamped systems are stable and non-oscillatory, their response is slower to reach the final value than critically damped or underdamped systems. Designers must balance the desire to suppress overshoot against the need for a timely response, as excessive damping can lead to sluggish performance.