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

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.

br3098

Mass is best added distributed along the arm ...

Perhaps ...

... but will have the most effect closest to the fulcrum.

No, the opposite is the case. The further from the fulcrum, the greater the effect of the mass. The pickup arm works as a lever.

Dear @cleeds  : Maybe @br3098 is refering that near the fulcrum makesthe tonearm has more operationsl stability but agree with you about modified the effective mass.

R.