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

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.

Dear friends @lewm  : as I said to complicated to be really precise or to achieve/have numbers in the subject because exist several parameters to take in count during play and we have to remember that even if we can't see the cartridge bounce all happens at microscopic levels and no matters what numbers says we really don't know what is down there happening.

Cartridge has its own resonance frequency between the: cantilever/stylus and the fulcrum in the suspensiion where the cantilever is atached.

The next thread is interesting for the gentlemans that want to confirm what they already know or that want to learn a little more on the subject:

http://www.vinylengine.com/turntable_forum/viewtopic.php?f=18&t=78564#:~:text=Principle%3A%20To%20measure%20actual%20tonearm,effective%20mass%20of%20the%20tonearm.


Regards and enjoy the MUSIC NOT DISTORTIONS,
R.

Raul, I guess we are all guilty of what we call in English "talking past each other", which means not paying attention to what the other guy said.  I fully agree that no calculation based on pure physics will really predict how a given combo of tonearm and cartridge will behave in practice.  The numbers are only a starting point.  This is why I pay no attention to the notion that if your calculated resonant frequency is not between 8Hz and 12Hz, the match is poor.  It's well and good to use the numbers as a guide, but that's all they're good for.  So, I think we agree.
I AM kind of a math guy, so it is interesting to me to note that the resonant frequency depends upon the square root of the quantity M*C, where M = effective mass, and C= Cartridge compliance (at 10Hz).  Because of the dependence upon the square root, there are actually a very wide range of values for both quantities that will work to fulfill the 8 to 12Hz desired endpoint.  For fun, one can play with one of the on-line calculators to see what extremes you can get away with.  But the fact is that few of us really know what the effective mass of our tonearm plus cartridge plus hardware actually is, due to all that was already discussed, and even cartridge compliance probably varies from sample to sample and according to the age of the cartridge.

mijostyn

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.

No, that is completely mistaken, and is one of the reasons many pickup arms offer counterweights of different weights. That’s because a factor in effective mass is the distance between the counterweight (actually, the counterweight’s center of mass) and the pickup arm pivot.

@lewm I think you misunderstood my reply. I was not insulting you and was not implying that you pasted from a text. I was saying that I was trying to avoid doing that myself. I apologize if my meaning was not clear.

I will restate my point: adding mass to a tonearm can be beneficial. But adding mass at the headshell (farthest point from the fulcrum) is problematic, will result in increased instability at the point of contact (stylus) and will not significantly alter resonance issues to the entirety of the tonearm. Mass is best added distributed along the arm but will have the most effect closest to the fulcrum.