Why the woofer moves badly when playing certain LPs

One fairly simple explanation for the complaint is the cartridge has compliance too high for the mass of the tonearm.

Have you looked at the records to ensure they don't have any warping, or that they are sitting flat?

You are getting the woofers pumping due to feedback.  The stylus is picking up the airborne sound and re-amplifying it.  Either relocate your turntable, try different platforms and if all else fails, buy a KAB Rumble Filter for $179.00 from KAB. That is what I had to do and now I am a very happy camper. 

Welcome starbusters to the whacky world of analog playback, where everyone has a theory and the laws of the universe believe it or not actually allow all the seemingly conflicting theories to be right. Is it right to leave the dust cover on? No. Except when it is. Or yes- except when its not!

Are you even having a problem? Yes, if it bothers you. No, if it doesn't. A certain amount of very low frequency woofer excursion with records is perfectly normal. Its also perfectly normal that some records are better than others. Not just in this but in every conceivable way. Sorry, ESL, conceivable means every way you can think of. 

There's things you can do to have less. stereo5 mentioned acoustic feedback which he should know is not what you have but remember the whacky universe he is right its something that can be a problem. Just not in your case. Also probably not in your case is record warp. Really obvious warp you can see. Less obvious is dips and bumps that are hard to see. But it doesn't take much, a tiny invisible dip when amplified comes out a half an inch at the woofer. Sometimes a record clamp might help.

Sorry but you just never know. That's why you get five, ten different guesses. Any one or all of them could be right. Or wrong.

Only way to know for sure is to learn by trying. If the woofer moves a lot but doesn't rattle the house and doesn't bottom out the voice coil I recommend write it off as just another one of vinyls many charms. Or you could complain and try another record. When two or three all play the same you will learn. Or if the next one is better you will learn that too.

So much more fun than boring old CDs don't you think?

millercarbon

... A certain amount of very low frequency woofer excursion with records is perfectly normal ...

Perhaps it’s "normal" for your system, but that needn’t happen in the absence of a signal and if it does, you’re wasting amplifier power and introducing distortion. My system is flat to below 20 hZ and I have no such problem, but I also pay a lot of attention to phono setup and matching phono cartridge to pickup arm.