good online resources for 2nd-order system dynamics

Question

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

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

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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.

Answer 1

Searching in Google itself gives you a great deal of information. I got this link which explains has the content which you need.

• http://www.facstaff.bucknell.edu/mastascu/econtrolhtml/SysDyn/SysDyn2.html

Next, [redacted: inappropriate link to pirated content] is an excellent source for those who are in need of books online.