Why the woofer moves badly when playing certain LPs

I would check external things like what the table is sitting on and how far it is away from the speakers and don’t forget the floor. Tonearms just don’t  play the record. They can pickup the room environment. The floor can be a big culprit sending the bass waves straight through the tonearm causing the woofers to move.  

Have you checked to see how low your woofer is supposed to go before your excursion is too much?

The resonance mechanism you and others propose involves forced vibration in which some source of periodic excitation acts close enough to the resonant frequency of the tonearm/cartridge to excite resonant response. This is a plausible explanation, although it doesn't explain the noticeable discontinuity in the woofer oscillations, roughly (exactly?) once per revolution, in the video. In other words, I see two distinct periods in the video. The shorter period corresponds to the woofer oscillations, the longer period corresponds to the very regular disruption of the woofer oscillations at about 0.5 Hz.

The mechanism I'm proposing doesn't involve resonance. The warp acts like a mild ski jump that imparts a vertical acceleration to the cartridge/tonearm once per revolution --- enough to flex the cantilever but not enough for the stylus to lose contact.

If the cartridge has too high a compliance (too low a mechanical resonance) then it will behave as you describe. If the cantilever is stiffer (less compliance) the mechanical resonant frequency will be higher and thus the amplitude of the warp energy will be reduced. Or- if the mass (not the tracking pressure) near the stylus is reduced (by changing out the hardware and getting rid of the stylus guard if there is one) the effect is the same.

Ish_mail, I shall assume you have an SME. Great table. Great clamp.
I am not sure what it would take to bottom out a Clearaudio bearing but they do make a peripheral clamp for their tables so I would assume that it works OK. I do not think I can tell much difference between reflex clamping and vacuum (I have both). Certainly, the vacuum method subjects the record to less stress but I have never seen a record cracked by reflex clamping. The SOTA vacuum system is brilliant but admittedly more complicated than a reflex clamp. The Michell reflex clamp will work with just about any turntable playing 130 gm or less records But when it comes to 150 grams and up you have to push down so hard on the bearing to flex the record into the platter you might eventually damage the bearing. The threaded version you have is brilliant, just hold the platter and tighten it down. 

Cleeds, what your equipment is speced at has nothing to do with your system's bass performance. Judging by your opinion you do not have any bass. Impulse test your system. I'll bet there is nothing below 40 Hz. 

mijostyn

Cleeds, what your equipment is speced at has nothing to do with your system’s bass performance.

I’d agree, but only to a point. The specs merely indicate a component’s potential, according to the manufacturer, and are certainly no guarantee of actual performance. That’s why component matching and system setup are so critical.

Judging by your opinion you do not have any bass. Impulse test your system. I’ll bet there is nothing below 40 Hz.

I understand why you say that, because you’ve previously stated that, "anyone who listens to vinyl and has a subwoofer system needs a subsonic filter." Apparently your system has some rumble problems that cannot otherwise be ameliorated. But my system doesn’t have that issue, and I can get more than a full octave below 40 hZ from LP. We are talking down into LF that really can’t be heard, but only felt.

It’s not easy to get good, clean, flat LF performance from LP, but that doesn’t mean that it can’t be done.