Unterdämpfte

Unterdämpft is a German term that translates to "underdamped" in English. It describes a type of oscillatory behavior in a system where the damping is insufficient to prevent oscillations from occurring. When a system is underdamped, it will overshoot its equilibrium position after a disturbance and then oscillate back and forth with decreasing amplitude. Eventually, due to the presence of damping, the oscillations will cease, and the system will return to its stable equilibrium.

This type of damping is commonly encountered in physical systems such as mechanical oscillators, electrical circuits, and control systems. For example, the suspension system of a car is designed to be underdamped, allowing the wheels to oscillate after hitting a bump but eventually settling down. In electrical circuits, an RLC circuit can exhibit underdamped behavior depending on the values of its resistance, inductance, and capacitance. The characteristic equation of a second-order linear system is often used to determine whether the system is underdamped, critically damped, or overdamped. An underdamped system is characterized by complex conjugate roots in its characteristic equation. The rate at which the oscillations decay is determined by the damping ratio. A smaller damping ratio indicates slower decay and more oscillations.