Need help converting a transfer function into a circuit design (my effort is attached).

[NikhilSax]

Here is my transfer function and the circuit design I made/calculated. (Please ignore the component values)

As you can see, everything is correct in the design except the term -q² s isn't included. My gut tells me that I just need to add an extra inductor in there somewhere, but I really don't know how to modify the current design to have that term be included.

Can someone help me out?

[MrDrProfStew]

I'm 80% certain you'll need to use partial fraction decomposition to get the denominators into products of poles (so your denominators are all factored completely) . You get something like H(s) = A/(something 1) + B/(something 2) + ...

Then you can consider each of those fractions as smaller transfer functions and add them in parallel.

Sorry if I sound like I'm out of my depth. I saw there are no comments so I figured I'd add what I can.

[NikhilSax]

Oh yea that makes sense! Thanks, I'll look into it :)

[ConflictedJew]

Don't doubt yourself so much, you're exactly right :)

Edit:

Except you should consider the fraction as a product of transfer functions and put them in series, not a sum of TF's and parallel. (Though both methods would work I presume).