Tone arm resonance and cartridge compliance: How do they interact??

The short answer is you determine by seeing if the screws fit. They usually do.

The long answer: Been running analog since the 70’s. Know all about just what you’re talking about. Its never been a factor.

Main reason it matters, audiophiles are all over the place trying all kinds of goofball stuff instead of just going with what works. So every once in a while some guy matches one oddball arm with one quirky cart, it sounds funny, some wise guy says yes compliant this with low mass that, and everyone succumbs to the tech talk. When in reality that’s not it, as invariably is proven ten minutes later when some other guy says hey I run that same cart, on that same arm, it sounds the bomb. They then technobabble back and forth, never getting anywhere.

So what I do instead, look at output, read listening impressions, go for what sound best matches my preferences. Never failed me yet.

Increasing arm mass lowers resonance frequency. 

Years ago I had a high compliance cartridge matched with a high mass tonearm. I was always blowing woofers. Yes it does matter to match the arm and cartridge. This chart from the Vinyl Engine will give you an idea if the cartridge and arm will work together!!
https://www.vinylengine.com/cartridge_resonance_evaluator.php?eff_mass=25&submit=Submit

What yogiboy said, +1.

After so many years of posting this link people still asking the same question. There is an answer. 

The most common mistake is to make a wrong calculation using a compliance figure printed in the cartridge manual if this compliance measured at 100Hz, because for correct calculation we must know a compliance measured at 10Hz. 

If you see dynamic compliance measured at 100Hz first you have to do is to convert it to 10Hz using x1.7 formula. 

Then follow instruction in this link.  

To measure actual resonance of your particular cartridge and tonearm you need a Hi-Fi News Test LP, this is the only was to see what is the resonance and what's going on with a cartridge and tonearm in this situation: 

"Tracks 2 & 3: Cartridge & Arm, Lateral & Vertical Resonance Test
These two tracks are used to test the resonant frequency or your tonearm and cartridge combination in both the vertical and horizontal domains. These tracks offer both a visual and auditory indication of the resonant frequency; the stylus will “wobble” and the test tone will warble. A resonant frequency between 8 - 15Hz is ideal."