I am trying to determine the resonance frequency of an RLC resonator with added capacitor, as shown below:
simulate this circuit – Schematic created using CircuitLab
Two cases are easy to determine:
$$Rp=0 \rightarrow \frac{1}{\sqrt{LsCs}}$$ $$Rp=\infty \rightarrow \frac{1}{\sqrt{Ls\left(\frac{1}{1/Cs+1/Cp}\right)}}$$
Now I'd like to derive a formula that includes Rp. How should I approach this?