Second Order Transient Circuit
  • Characteristic Equation

$s^2 + 2 \zeta {\omega}_0 s + {\omega}_0^2$

$s_1 = -\zeta {\omega}_0 + {\omega}_0 \sqrt{{\zeta}^2 - 1}$
$s_2 = -\zeta {\omega}_0 - {\omega}_0 \sqrt{{\zeta}^2 - 1}$

$x_c(t) = K_1 e^{s_1 t} + K_2 e^{s_2 t}$

  • $\zeta > 1$ overdamped
  • $\zeta < 1$ underdamped
  • $\zeta = 1$ critically damped
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License