Magnitude of transfer functions of two filters
Take the first example and make life a little easier by simplifying it. For instance, it can be shown that R and Rp can be combined into a single series resistor being fed from a new voltage source that is reduced by the potential divider ratio. You then get a new circuit that looks like this: -



Clearly the value R in the above is the parallel combination of the two resistors in the original question. Solving: -

G(s) = \$\dfrac{\dfrac{\dfrac{sL}{sC}}{sL+\dfrac{1}{sC}}}{R+\dfrac{\dfrac{sL}{sC}}{sL+\dfrac{1}{sC}}}\$ = \$\dfrac{L/C}{L/C+sLR+R/sC}\$

Multiply through by sC to get \$\dfrac{sL}{sL+s^2LCR+ R}\$

And finally G(s) = \$\dfrac{s\dfrac{1}{CR}}{s^2+s\dfrac{1}{CR}+\dfrac{1}{LC}}\$

To get back to the original TF you need to reduce the above TF by the voltage potential divider formed by the original R and Rp.