# good online resources for 2nd-order system dynamics

I'm looking for good online resources for 2nd order system dynamics. Any recommendations?

I'm looking for stuff that ideally includes discussion of Q, damping ratio, overshoot, bode plots, for systems with transfer functions of

$$H_1(s) = \frac{1}{\tau_2^2 s^2 + \tau_1 s + 1}$$

$$H_2(s) = \frac{\tau_1 s + 1}{\tau_2^2 s^2 + \tau_1 s + 1}$$

and

$$H_3(s) = \frac{s}{\tau_2^2 s^2 + \tau_1 s + 1}$$

edit: I've done change of variables to rewrite as

$$H_1(\sigma) = \frac{1}{\sigma^2 + 2\zeta\sigma + 1}$$

$$H_2(\sigma) = \frac{2\zeta\sigma + 1}{\sigma^2 + 2\zeta\sigma + 1}$$

and

$$H_3(\sigma) / \omega_0 = \frac{\sigma}{\sigma^2 + 2\zeta\sigma + 1}$$

where $\sigma = \tau_2 s = s / \omega_0$, $\omega_0 = 1 / \tau_2$, and $\zeta = \tau_1 / 2\tau_2$ to normalize out the time scaling factor and end up with a transfer function of the single variable $\zeta$ (damping factor) which I think is the conventional treatment.

• Community Wiki.
– anonymous
Commented Oct 1, 2010 at 18:00
• done. (.......) Commented Oct 1, 2010 at 18:20