Second-order system responses
Transfer: \(G(s)=\frac{K\omega_n^2}{s^2+2\zeta\omega_n s+\omega_n^2}\). Use sliders to change \(\zeta, \omega_n, K\). Plots: step & impulse. Poles shown in s-plane.
Natural frequency ω
n
(rad/s):
2.0
Damping ratio ζ:
0.25
DC gain K:
1.0
Sim duration (s):
10
Pause
Reset t=0
Case:
Underdamped
Formulas used: analytic inverse Laplace. Step: y(t) depends on ζ cases (underdamped/crit/overdamped).
s-plane: poles indicated (×). Imag axis vertical, Real axis horizontal.