Tone arm resonance and cartridge compliance: How do they interact??

I have the test record mentioned by Chakster, it was thrown in when I bought my last cartridge, an SPU Royal N. Before fitting the SPU to my arm (Schröder) I ran my Proteus through the resonance tracks. Arm eff mass 13g, compliance 13, cartridge weight 7.8g, 0.9g for the screws (I weighed them). The Vinylengine calculator https://www.vinylengine.com/cartridge_resonance_evaluator.php?eff_mass=13&submit=Submit gives a resonance frequency of 9Hz for this combination, on the test record there was warble from 14Hz down but visible wobble only at 7Hz. Fitting the SPU involved changing an aluminium cartridge mounting plate for a brass one, this raises the arm’s effective mass to ~18g plus whatever effect moving the counterweight half an inch further back has but I’ll ignore that. So for the SPU eff mass is 18g, cartridge and the adaptor that comes with it 15.9g,screws and nuts 1.5g and the compliance 8. This gives a resonance from the calculator of between 9 to 10 Hz, on the test record I initially didn’t see any wobble with the setting roughed in but after a couple of weeks of fine tuning by ear I ran the test again and this time it wobbled at 7Hz. The Korf calculator, which I hadn’t found until later, offers an explanation for what is going on.

10+ chakster. Forget about equations. Use the darn record!
 It is always best to start with a light tonearm. It is easy to add mass, much harder to take it away. You want to get your resonance point between 8 and 10 Hz for the best bass. When the cartridge gets to the resonance frequency you will see it start to bounce. You simply add mass until you get the resonance frequency down where you want it. There are head shell weights and Soundsmith sells a set of graduated head shell screws that are brilliant.
Effect. If the resonance frequency is too low the tonearm can bounce into the air when it hits a warp. Too high and your bass performance declines and you invite acoustic feedback. When you turn the volume up the system starts to howl. 

Dear @mijostyn : "  Use the darn record! "

Really, because exist no perfect recorded LP and in that so imperfect medium with so many different parameters involved and full of resonances/vibrations/noises/distortions developed how can you trust in what is supposed to be measured ! ! 

Regards and enjoy the MUSIC NOT DISTORTIONS,
R.

I am surprised no one has mentioned yet that the tonearm has no intrinsic resonance, because the only resonance it has that you care about is the resonance  with the cartridge bolted onto it. The effective mass of the tonearm is equal to the basic effective mass plus contributions from the cartridge, the head shell, the cartridge screws, and where the counterweight is located. That’s why in the end few of us really know exactly what is the effective mass to which we are coupling our cartridges. Finally, the resonant frequency is a product of the effective mass multiplied by the compliance of the cartridge after you take the square root of that product and invert it.So, high mass and high compliance both have a tendency to reduce the resonant frequency. There is an inverse relationship.