Finding the resonant frequency of a RLC circuit with a tweeter
There are two approaches for these (simple) transfer functions: brute-force or the fast analytical circuits techniques abbreviated FACTs. I will show you both for the first example and leave the second to you. In the first example, you see how the series connection of \$C_1\$ and \$R_1\$ - \$Z_1(s)\$ - loaded by the parallel arrangement of \$L_1\$ and \$R_2\$ - \$Z_2(s)\$ - (the tweeter) form an impedance divider. You can thus immediately write that:

If you carefully develop this expression, you obtain the transfer function linking \$V_{out}\$ - the voltage across the tweeter - to \$V_{in}\$, the excitation voltage and this is \$H_{ref}\$ in the above figure. From there, you will have to collect the terms in the denominator and arrange the whole thing in a second-order polynomial form \$D(s)=1+\frac{s}{Q\omega_0}+(\frac{s}{\omega_0})^2\$. In this expression, \$\omega_0\$ is the natural resonant frequency you want.
As you can see in this approach, which is still fairly simple, you need to write algebra lines to get to the result in an unordered form. Further work is necessary to factor the expression in a so-called low-entropy form. For instance, you don't immediately see the attenuation a high frequencies in \$H_{ref}\$ and further work is necessary. The FACTs, on the other hand, will shield you from writing algebra lines, especially with passive circuits like this one. All you have to do is split the circuit in small individual sketches you will solve and assemble in the end. Should you make a mistake, fix the guilty drawing and there you go. The principles are described in the book I published in 2016 and in a seminar I taught at an APEC conference. The FACTs consist of determining the time constants of a circuit observed when a) the stimulus is zeroed and b) the output is nulled (no ac excitation reaches the output). You first start with \$s=0\$ in which the capacitors are open and the inductors short circuited. To determine a time constant, you temporarily remove an energy-storing element and &quot;look&quot; through its terminals to determine a resistance \$R\$. That resistance is then used to express the time constant involving the considered element: \$\tau=RC\$ or \$\tau=\frac{L}{R}\$.
The below diagram shows the first circuit explored using the FACTs. You determine the resistance in all cases by inspection: no algebra, just infer the resistance by reading the sketch:

Once you've done this simple exercise, you can assemble the pieces as in the below Mathcad sheet in which you see that the denominator naturally comes in a well-ordered form:

The resonant and peaking frequency are given in the sheet. The first one corresponds to the natural oscillations without damping or an infinite \$Q\$ while the second one indicates where the magnitude peaks. You can plot the response and see that both first and second approach match well:

It is important to write the transfer function in the correct form, where the leading term corresponds to a gain. Here, you see that in \$H_{final}\$ what the gain is when \$s\$ approaches infinity; you also see the resonant frequency and the quality factor while none of these parameters showed up in the brute-force expressions. The FACTs require practice to acquire the skill but once you have it, you won't return to the classical approach. As a next exercise, you could now apply the FACTs to determine the input and output impedances of this network and see how they come quite quickly.