Undamped System

Topics: Feedback Control Systems

An undamped system corresponds to $\zeta = 0$ in the standard form.

Transfer function

$T(s) = \frac{\omega_n^2}{s^2+\omega_n^2}$

Step Response

$y(t) = 1 - \cos(\omega_n t)$
The system oscillates at the undamped natural frequency $\omega_n$. As the name undamped indicates, the oscillations are not reduced; they are sustained.

Poles

The system has 2 imaginary poles at $s= \pm j\omega_n$.