Once three weeks ago a mysterious loud vibrating noise showed up. Lasted a few doses and went away. Came back again same day I purged and it stayed gone. It happened a few times 3 days ago. Yesterday however it stayed around until I purged completely.
It isn't anything to do with burrs as you can see in the video with grinder completely opened up.
It seems to come from lower part of grinder.

Three videos. 1) with hopper making noise/vibration
2 with hopper operating without noise
3 opened up with the noise/vibration

Did you open up the bottom? My SJ has a seriously thick base plate which might just sound like this if it came loose over time, also could be something inside that is coming loose, the doser, the starter cap etc etc.

Usually this seems to happen when the pin for adjusting the collar is loose.
Every Mazzer I've used regularly has made this sound at least sometimes. I wouldn't worry about it.

Edit: Your third video seems to show that this might not be the case. But also, I don't know how these grinders normally sound run without beans or a collar, so I can't tell if it's any different from otherwise.

Did this vibration stop? I have a robur at my house and I had the same problem. I think I figured out what was causing it-- regardless if I know what the problem is, I seem to be able to fix it by hitting the manual button very rapdily about 20 times. I live in Texas and it when it is humid outside, I get this problem. When it is dry, I do not.

My theory is since I dont use it as often as a high volume shop, moisture in the air causes the contacts on the relay to get a tiny bit of build up on it. When this happens and you call for a grind, the relay closes, but chatters slightly because of this build up- this chatter may be the vibration you hear. By pressing the button over and over, it may perhaps cause the buildup to come off due to the friction.

I still get this every once in a while and I am always able to get rid of it by doing this. Just FYI

I can't remember for sure, but I think these may have run capacitors, If so and one is going/has gone bad or got a bad connection, then it could make the motor sound like that....with the motor sounding like a bearing has failed or out of balance. You can also loose some torque.

I recently repaired my extractor hood which had a bad start/run capacitor, it sounded like bad bearings and ran for years almost like it from new. It got worse and worse and one day simply wouldn't run any more. I took the cap out it was distorted and had finally exploded through the side. A few dollars and a new cap and she ran sweetly again with more power and none of the noise.

Worth checking out perhaps.