dampingunderdamped

The term "underdamped" describes the behavior of a system that oscillates with decreasing amplitude when disturbed from its equilibrium position. This is a common characteristic in systems exhibiting oscillatory motion, such as a pendulum, a spring-mass system, or an electrical circuit with inductance and capacitance. When an underdamped system is perturbed, it will swing back and forth, but each subsequent swing will be smaller than the previous one. This reduction in amplitude is due to energy dissipation, which is present in all real-world systems to some extent.

The rate at which the oscillations decay in an underdamped system is determined by the damping coefficient. A lower damping coefficient results in slower decay and a greater number of oscillations before the system comes to rest. Conversely, a higher damping coefficient leads to a more rapid decay and fewer oscillations. If there were no damping at all, the system would oscillate indefinitely with a constant amplitude, a theoretical state known as undamped oscillation. The underdamped condition lies between the extremes of no damping and critically damped (where oscillations cease immediately) or overdamped (where oscillations are suppressed and the system returns to equilibrium slowly without oscillating). The presence of underdamping is mathematically characterized by the roots of the system's characteristic equation having a negative real part and an imaginary part.