weird feeling macbook pro

What is your MBP's model? And does the vibration start/stop immediately after you plug/unplug MagSafe?

Few have reported this problem here.

Try to use the 3 pronged plug. Connect it to a grounded outlet.

This is not dangerous.

Best.

I see. The reason I asked the model was to figure out whether you have a SSD or a Hard Disk Drive (HDD).

Naturally, HDDs spin and can cause vibrations. It could also stop once you disconnect MagSafe (granted no data is being written/read) to preserve battery but it is not instantaneous This is why I asked whether it's immediate or not. Similarly, disconnecting MagSafe could lower fan speed, another cause for vibration, especially if they're not properly installed which would be less noticable in lower speeds.

There is also the sensation of vibration (in contrast to actual physical device vibration). Possible electrical issue. This seems to be your case. I recommend you take it to Apple. If there is a leak of some kind it could of course damage electrical components.

Apple Store or an Authorized Service Provider would do.

Not an electician, but I'd guess if you manage to use a cord/wire to ground your MBP and vibration doesn't happen anymore, that proves the source was a leak.