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

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. 😁

br3098, You are confusing two different things.  roberjermain is correct, and I wrote the same thing, a few posts above yours.  BOTH increasing tonearm effective mass and increasing cartridge compliance will decrease the resonant frequency of the system.  If you will look at the equation, you will see that the product of the two quantities is inversely proportional to Fres.  Now, what bdp and you are talking about does not per se alter the resonant frequency, as long as you don't change effective mass and compliance. What damping and choice of materials does, if done smartly, is take the energy of the resonance that will occur at the calculated frequency and spread out or broaden the resonant peak, the range of frequencies at which the energy of resonance is dissipated, which is usually a good thing that can mitigate an otherwise bad pairing of cartridge and tonearm.  And yes, the (distance from the pivot to the center of mass of the CW)-squared times the mass of the CW, adds to effective mass.  That's why, if you want to minimize effective mass, you want a heavy CW that can be moved as close as possible to the pivot. (Because the em will vary as the distance-squared but only in direct proportion to CW mass.)

The beauty of the adjustable-mass counterweight of the Zeta arm (accomplished via removable steel discs in the hollow counterweight) is that if one wants to use the arm in it's lowest effective mass guise, more discs are placed in the counterweight and that cw is placed as close as possible to the arm's bearings. For higher em, fewer discs and the cw further away. Counter-intuitive, but true.