04 - Second Order Systems

The characteristic equation of second order system is given by \[\tau^2s^2 + 2\zeta\tau s + 1 = 0\] \[\begin{aligned} \text{If \ } \zeta &< 1 \qquad \text{underdamped system, roots are complex} \\ \zeta &= 1 \qquad \text{critically damped system, real and equal roots} \\ \zeta &> 1 \qquad \text{overdamped system, roots are real} \\ \zeta &= 0 \qquad \text{undamped system, complex roots with zero real part} \end{aligned}\]