underdempede

Underdempede is a term used in engineering and physics, particularly in Danish and Norwegian contexts, to describe dynamic systems whose damping is insufficient to prevent oscillation. In English the equivalent adjective is "underdamped." An underdamped system responds to a disturbance with oscillations whose amplitude decays exponentially over time.

Mathematically, underdamping occurs when the damping ratio ζ satisfies 0 < ζ < 1. For a second-order linear system with natural frequency ωn, the response oscillates at the damped frequency ωd = ωn sqrt(1 − ζ^2). The transient behavior typically includes overshoot and ringing before the system settles to its steady-state value.

Common examples of underdamped systems include mechanical mass–spring–damper assemblies with light damping and electrical RLC circuits where resistance is too small to critically damp the oscillation. In control and design, underdamping may be acceptable or even desirable when a fast response is required, but it can also cause stability issues, excessive stress, or poor precision. Designers adjust damping through mechanical dampers, resistive elements, feedback control, or other means to trade off between speed of response and oscillatory behavior.

Related concepts are critically damped (ζ = 1), which returns to equilibrium fastest without oscillation, and overdamped (ζ > 1), which returns without oscillating but more slowly.