Arm resonance - the anal way

J!m

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#41
Arm's effective mass is nothing but a sum of effective masses of every part.
You had me until the end. This is an oversimplification of what’s going on.

Mass at distance from pivot summed is about as simplistic as I could describe it.

Example: 100 gram arm that is eight inches long compared to a 100 gram arm that is nine inches long. Same mass but very different effective mass. (Ignore the compliance/flexural component)
 

laatsch55

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#42
Ya'll are starting to sound like a bunch of oilfield pumping unit hands arguing about "counter balance effect" Counter balance Moment" static balanced, dynamic balance....
 

Makymak

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#44
... starting to sound like...
:)

You reminded me of an old joke we said here...

"In a boat, in the middle of a lake, there are three passengers: one is a pro in biology, the other is a pro in physics and the third is a pro in maths. The first asked the boatman:
- Do you know anything about biology?
- No (replied the boatman)
- Pity, you've lost 20% of your life.
The second passenger asked:
- Do you know anything about physics?
- No (replied the boatman)
- Pity, you've lost 30% of your life.
The third passenger asked:
- Do you know anything about mathematics?
- No.
- Pity, you have lost 50% of your life.

Disgusted, the boatman asked:
- Do you all know anything about swimming?
- No (replied all the three passengers)
- Pity, you have lost 100% of your life.

And he turned the boat upside - down... "
 

borchee

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#45
I think this is what Micro Seiki was trying to address with this tone arm design. Although they don’t really provide any data on how to adjust it.
Excellent, thanks!

I knew about it (although it wasn't Micro Seiki...here's a new one) but couldn't find it. If dimensions and mass of the sliding weight and counterweight are known, effective mass/resonant frequency can be calculated for different positions of them. I don't know the arm's actual range - effective mass with weights being at closest/farthest to the pivot...I mean if it goes from a light arm to a heavy one. If it does, my "concern" about the difference, when caltulating with mass instead effective mass, is pointless - just pick any cartridge, measure and adjust frequency by moving both weights.

EDIT: I read the instructions and it seems it can be adjusted throughout a wide compliance-range. Micro Seiki MA-707 effective mass adjustment.JPG
Ya'll are starting to sound like a bunch of oilfield pumping unit hands arguing about "counter balance effect" Counter balance Moment" static balanced, dynamic balance....
Well...the thread-title sums it up. :eek:
Example: 100 gram arm that is eight inches long compared to a 100 gram arm that is nine inches long. Same mass but very different effective mass. (Ignore the compliance/flexural component)
That's true, but you are talking two objects with different properties.
 

J!m

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#51
Just put the damn Cartridge on the Arm and Enjoy it! :evil4:
Kinda how we built cars in the 80's. Put it all together and then figure out what isn't optimal. Rear broke? OK we need to update that. Driveshaft looks like a barber pole? OK we need to upgrade that. Can't stop? OK we need to upgrade that. Motor mounts tore again? OK we need to upgrade that. Exhaust too loud? OK that's fine.

Best was a friends car- kept draining the battery but there were no significant electrical faults. (67 Dart GT). We had put in a 360 police interceptor motor and she pulled hard.

Turns out that it pulled so hard that the headlights would turn on, due to the weight of the solid (cast zinc I guess?) metal headlight switch knob. Not knowing they were left on all the time, the battery would naturally be drained if it wasn't dark enough out to notice they were on.
 

NeverSatisfied

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#52
EDIT: I read the instructions and it seems it can be adjusted throughout a wide compliance-range.
Seems even Micro couldn’t offer up a plug and play formula, they give you the ability to adjust the effective mass but you still have to use trial and error to get it right.
 

8991XJ

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#53
View attachment MA-707 Adj Mass in German.jpg
Seems even Micro couldn’t offer up a plug and play formula, they give you the ability to adjust the effective mass but you still have to use trial and error to get it right.
Yes they did offer some plug and play info so for a few cartridges you can set it and forget it!! I'm still digesting the info after translating it but here is the raw data for your use.
 

borchee

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#54
You had me until the end. This is an oversimplification of what’s going on.

Mass at distance from pivot summed is about as simplistic as I could describe it.

Example: 100 gram arm that is eight inches long compared to a 100 gram arm that is nine inches long. Same mass but very different effective mass. (Ignore the compliance/flexural component)
Hi J!m,

this is how the mass moment of inertia behaves. It's a simplified example, but the principle is correct. Let's say m1 is the cartridge, m2-4 is the arm and m5 is the counterweight.

Mass moment of inertia J!m correct index.JPG

The effective mass behaves the same way - will post equations, when time at hand.

EDIT: Messed up indexes below - corrected. Sorry for that.

Mass moment of inertia J!m incorrect index.JPG
 
Last edited:

NeverSatisfied

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#55
View attachment 59390

Yes they did offer some plug and play info so for a few cartridges you can set it and forget it!! I'm still digesting the info after translating it but here is the raw data for your use.
I am guessing those are all pretty well known cartridges, comparing other carts to them should yield some starting points?
I will weigh the sliding weight today and post the results.
 

J!m

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#56
I don’t see how changing distance (d^2) does not change effective mass.

If my remedial math skills are okay, you proved what I was indicating. Change d^2 and you change effective mass.

Or am I reading that wrong?
 

borchee

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#57
I might have misunderstood you due to the language-barrier at my end. Yes, of course distance affects effective mass and resonant frequency.

I wanted to show that the moment of inertia/effective mass of a body (tonearm + counterweight + cartridge + shell + screws + shims + what-not) is equal to the sum of moments of inertia/effective masses of each part the body consist of.

BTW, my math/physics skills are just as remedial as yours. This is not my everyday-bread, so it takes quite an effort to renew them...for the both of us, I guess.
 

J!m

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#58
Yeah, all I was saying is moving the identical mass (say the cartridge) in the headshell (changing distance) has an effect on effective mass.

also, changing the mass (with different screws in my example) also changes it, but to a lesser degree than distance does, because distance is squared in the equation.

So longer effective length, with Bayerwald/Lofgren A, compared to other alignments, you can not only reduce tracking distortion (slightly), but also effect effective mass. Usually a win-win but not always of course. It is on my Planar3 apparently.

I also use the Michell underslung counterweight which keeps the center of its Mass closer to the stylus tip plane. Minor improvement by eliminating the (possible) reflections off the counterweight when it is on arm axis as well. But that’s a different can o worms…
 

8991XJ

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#59
Moving the cartridge or using different cartridges isn't going to change the rotation of the earth much. What are we talking a few mm to or from the pivot point? What are we talking a few grams difference, 3 or so for something like the ortofon OM without the added weight plus a lightweight headshell so under 10 grams up to a ortofon spu in a big honking headshell or some heavy cartridge in a Fidelity Research 19 gram headshell so maybe a max around 25 grams. Mass of a cart/headshell is not universally centered or set up at some particular point but we are still just talking about a few mms change.

As stated earlier this is great to be able to get to the bottom of the topic but since the resonance frequency is good to go anywhere from 7-13Hz, in most cases, all I really want is the proper 10Hz compliance from the Japanese cartridges.
 

8991XJ

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#60
I am guessing those are all pretty well known cartridges, comparing other carts to them should yield some starting points?
I will weigh the sliding weight today and post the results.
Some of those are well known, but all older cartridges. It is interesting that some with high compliance have the weight moved way out on the arm...increasing the effective mass which is opposite of what we might think is the proper set up. That is why I need to evaluate the info as it appears to smear the ideal result all over the map even though MS says in the instructions for their MA-707 that 10Hz is the ideal resonance frequency.
 
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