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

lewm, I agree and disagree with different parts of your statement. Rather than cut and paste a text on mechanical amplifiers and resonance, please tell me how adding weight at the headshell is beneficial to the resonance of the lever?

I agree that increasing the mass of the lever (arm tube) will dampen a mechanical amplifier. But increasing the resistant load will have the opposite effect, decreasing stability and increasing secondary effects (hysteresis, etc.) Ideally, you would change the mass of the tonearm buy using arm tubes of differing weight and matched headshells. Some manufacturers used to do this.

If you are going to stabilizing mass to most conventional tonearms, adding it as close as possible to the pivot point will both increase stability and lower resonance.

@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.

The pickup arm works as a lever

Exactly. And the further mass is added away from the fulcrum the more destabilizing the effect. Resonance (the original topic of this post) is increased. A pivoted tonearm is not just a lever, it's a mechanical amplifier.

I'm not saying that adding mass to the headshell does not have benefit. But there are also detrimental effects. From the perspective of decreasing resonance and other artifacts the best of all worlds is to increase total mass uniformly and proportionally across the entire length tonearm and headshell. Barring that, adding weight to the tonearm closest to the fulcrum will have the most damping effect and reduce resonance frequency change.

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. 😁

@lewm @cleeds 

Gents, my diatribes were only in regard to the OPs question regarding resonance. Obviously adding mass further out from the fulcrum is the most effective use of mass, but (as I described) is problematic for mechanical reasons and is not the most effective method of reducing resonance amplitude. Calculating the change in resonance magnitude will require additional information not provided.

Now if, as lewm proposed, we are allowing the alteration of other factors including "damping, stiffness, materials used" then all bets are off. I hadn't realized that we were discussing a tonearm with an infinite k value. 😁