A standard continuous-time second-order system can be written as

$$H(s)=\frac{K\omega_n^2}{s^2+2\zeta\omega_n s+\omega_n^2},$$

where $\omega_n$ is the natural angular frequency and $\zeta$ is the damping ratio.

The poles are

$$s=-\zeta\omega_n\pm\omega_n\sqrt{\zeta^2-1}.$$

Their locations produce three familiar regimes.

For $0<\zeta<1$, the poles are a complex-conjugate pair and the transient is underdamped, with decaying oscillation.

For $\zeta=1$, the repeated real pole gives critical damping.

For $\zeta>1$, two real negative poles give an overdamped nonoscillatory response.

The natural frequency sets the characteristic time scale, while the damping ratio controls how oscillatory the transient is. The same normalized form appears in mechanical vibration, RLC circuits, filters and feedback systems.