It is NOT cartridge/arm mismatch. Ported speakers are a bit more susceptible to this. My old Aerial 10ts would do the woofer dance very well. Make sure your amp has enough headroom so you don't get clipping, put the covers back on the woofers. Stop watching them. The suggestions for a subsonic filter are good, but I have not heard one that didn't seem to damp things too much. It could work for you. You might have some success experimenting where the speakers are placed, but you probably can't eliminate it completely.
I have two, 18" drivers handling the duties down low. On a lead-in of a slightly warped record I can feel them pressurizing the room from side to side. :-)