tonearm resonance

[allears]

My experience comes from making musical instruments , and the ones I'm thinking of are marimbas or xylophones. These have keys that are tuned to vibrate at a certain pitch as their fundamental resonance , and this depends on their springiness , their length and the weight of the ends . A key is a simple block in most cases , and a block when struck vibrates in the manner shown , a wave with two nodes where the block hardly moves at all and three antinodes at the centre and the ends where it moves a great deal. The block can therefore be supported at the nodes without effecting it's ability to vibrate , and can in fact be held quite firmly there without damping the musical tone too much , whereas holding it anywhere else results in major damping .(get a 10"piece of 2x1 and hit it while holding with finger and thumb)(Or rest it on some foam with some sawdust on it and tap it and watch the dust collect at the nodes)
My point is that the tonearm is also supported at two points , one at the bearing which is very much in the right proportion of the length to be close to a node , and the other at the stylus which is exactly at the point where you would expect there to be an antinode and maximum movement. So the bearing position seems to be helping the tonearm vibrate and the stylus position seems to be where it can be most violently effected by that vibration.
Hm, I think I'll get a tonearm and try and do the sawdust trick with it and see what it reveals....otherwise , any thoughts on this?

[YNWOAN]

Very interesting :-) One thing that does occur to me though is that although the arm is indeed supported at the bearing and at the stylus, the manner of support is quite different. That is to say that at the bearing the support is very stiff and non compliant whilst at the cartridge the support is very much less stiff and much more compliant (the cartridge suspension).

[Conrad Hoffman]

The mass distribution is way different than the usual xylophone bar, so I wouldn't worry about that mode. I can envision other modes, and can't decide if tuned mass dampers (decoupled counterweights) are a good thing, or a bad thing. I've also thought about building an arm with almost all the distributed mass removed. It would be a light flexible flat plate, maybe carbon fiber, solidly fastened at the pivot so it could only swing side to side. The tracking force would be determined by how much it was bent (forced) upwards at the pivot, and the resonant frequency would be determined by adding mass at the cartridge end. The springy plate would need a certain amount of damping. It sounded good on paper, and addresses the bending mode at the pivot with a regular balanced arm, but it would have zero resistance to footfalls. There was a similar commercial arm at one time.