Transients

Transients are phenomena or signals that exist only for a limited period before a system settles into a later state of rest or steady operation. They arise when a system experiences a change in input or initial conditions and fade away as energy dissipates or constraints take effect.

In engineering and physics, transient response describes how a system reacts to a sudden change, such as switching a circuit, applying a step input, or a fault. Transients can be damped or oscillatory, depending on the system's damping, natural frequencies, and energy storage elements.

In linear time-invariant systems, the total response is often decomposed into a transient, or homogeneous, part and a steady-state, or particular, part. Transients typically decay over time, with the rate governed by time constants and damping ratios. Practical descriptions use measures such as rise time, settling time, and overshoot to quantify transient behavior.

Common examples include RC and RL circuits, where capacitor charging or discharging follows exponential transients with a time constant tau = RC or L/R. Second-order systems can exhibit underdamped, critically damped, or overdamped transients, influencing how quickly they reach steady state and whether oscillations occur.

Beyond engineering, transients also refer to short-lived physical events in other fields, such as optical or astrophysical transients that brighten briefly, or transient states in stochastic processes that are not recurrent. The term emphasizes temporariness and the distinction from long-term or steady phenomena.