Transfer function of an RLC circuit I'm trying to simulate an RLC circuit using transfer function. Circuit is there: http://i.stack.imgur.com/MC8ME.png (I'm a new user therefore I cannot post images)

But I can, L.Motl...
Main current (I) is the output and V is the input. So far, I'm stuck at this:

TF = (Q1(s) + Q2(s)) / ((30 + s)(Q1(s) + Q2(s)) + 20 * Q1(s))

I need to get rid of Q1 and Q2, but I cannot find a way.
 A: This circuit contains only passive components, and, by inspection, can be decomposed into series and parallel combinations.  You can solve it simply by writing down the complex impedance (as a function of frequency) for each of the components, and then combining those expressions using the usual rules for series and parallel combinations of impedances.
A: You must use Kirckhoff laws for alternate circuits. So, the tranfer function that you'll find can be used for any input signal, with Fourier Transform (because transfer function is the output of the system for a delta signal input in frequency domain).
We obtain:
$$\left\{\begin{aligned}
&V_I e^{i\omega t}= R (I_1(t)+I_2(t)) + j \omega L (I_1(t)+I_2(t))+ R I_1(t) \\
&V_I e^{i\omega t}= R (I_1(t)+I_2(t)) + j \omega L (I_1(t)+I_2(t))+  \frac{1}{j \omega C} I_2(t) \\
\end{aligned}\right. $$
 or, if you aren't interested to know $I_1$ and $I_2$ in separated rings you can consider the parallel of R2 and C:
$$V_I e^{i\omega t}= RI(t) + j \omega L I(t) + \frac{1}{\frac{1}{j\omega L}+ j\omega C}I(t) $$
Now, you haven't sayed where is Vout...but with these approach, you can easily calculate current and tension in every point of circuit.
