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

The different size counterweights are supplied so you can counterbalance different weight (mass) cartridges. You can not control resonance with different mass counterweights because once the cartridge is balanced you wind up with the same effective mass regardless of counter weight mass.
Now Raul, unless you are blind measuring resonance points with a test record is painfully easy. Your comment would leave me to believe that you have never set up a cartridge correctly.

The problem with calculations is that there is enough variation in tonearms and cartridges that the published specs may be off a little.
The record tells you what is really happening. But the resonance is not a sharp peak. It is a bell curve. The point where the cartridge starts bouncing is what you pay attention to. You know you are close when you hear the warble. Using the test record also gives you an idea of how severe the resonance point is. Some combinations barely move at the resonance point while with others the cartridge almost goes air born in which case it might have to be changed. I suspect it is a matter of damping.
Moment of inertia is different then effective mass. Longer heavier arms have higher moments of inertia. This really only creates issues following warps. If records are stored correctly very few should be significantly warped. Vacuum hold down and reflex clamping solve the problem under any circumstance. 

there is another moment - most of tonearms do have rubber gourmet or other means to isolate counterweight (s), so it has it's own resonance which can be measured.

 " Your comment would leave me to believe that you have never set up a cartridge correctly. "


You have no idea what you are talking about and this time as almost always your opinions comes from your imagination are what you figure about with no true foundations but your own experiences that could be some wrong because your misunderstanding on " something ". Do you think you own the audio Bible?

Sorry, no one has it and forgeret about that LP test and re-read what I posted to you because I think you are way wrong if think that even with vaccum hold down that LP test is PERFECT.

R.

br3098, If you wanted to insult me, you could not have done a better job than to accuse me of cutting and pasting from a text. ( You wrote, "I agree and disagree with different parts of your statement. Rather than cut and paste a text on mechanical amplifiers and resonance,...")  Whatever I wrote anywhere on this thread came out of my own head, and I take full responsibility for it, right or wrong.  I also am happy and willing to be corrected, if wrong.
Now, as to the second part of your inquiry, "please tell me how adding weight at the headshell is beneficial to the resonance of the lever", I'd be happy to respond if I could figure out what you are talking about.  Where did I claim that adding weight to a headshell was "beneficial" to resonance?  What I did say in response to Raul is that exchanging a heavy headshell for a lightweight one (or for that matter exchanging a lightweight headshell for a heavy one) has an "inordinate" effect on effective mass. By using the word "inordinate", I mean the effect on effective mass is nearly 1:1, since the headshell is right over top of the cantilever.  Whereas, adding mass anywhere else on the arm going back to the pivot point is of lesser consequence due to its distribution on the lever.  Effective mass is a quantity related to the distribution of the mass of the tonearm, not merely to its weight if you put the whole shebang on a scale. Do you disagree with that?  If so, state your case.