transient-response

Transient response is the time-domain behavior of a system following a sudden change (step, impulse, or pulse) in its input. It comprises three phases: initial reaction (rise time and overshoot), oscillatory behavior (ringing at the system's natural or resonant frequencies), and settling to the final steady-state value. The transient response is characterized by parameters including rise time, peak time, maximum overshoot, settling time, and decay ratio. It is fundamental to control theory, signal processing, and circuit design where rapid and stable system behavior is required. The transient response is determined by the system's poles in the complex plane — underdamped poles produce oscillatory transients, overdamped poles produce smooth exponential approaches, and critically damped poles produce the fastest non-oscillatory response.\n\n[formal: transient response | substrate: behavior | horizon: a life | explicit: yes | epoch: 1.00]