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

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.

Increasing arm mass lowers resonance frequency

@roberjerman, that's simply not true. It's a common misconception because resonance charts calculate frequency based on total arm weight. But resonance is a function of other factors besides weight; including stiffness, flexibility and damping. Putting a weight on the headshell will help to damp the headshell but not the arm tube. And weighting the headshell may actually result in worse performance. Probably not unacceptably worse but often measurable worse.

The tonearm is a level balanced on a fulcrum. If you take a counterbalanced lever of, let's say, 10 feet long, and increase the weight on both the headshell (effort arm) and the move the counterweight away from the fulcrum, will the resonance increase, stary the same or decrease (amplitude AND frequency stabilize or shift)? The correct answer is that amplitude will increase and frequency will shift. The same thing happens with a tonearm, but on a much smaller scale. 😁