Welcome to BGW!
FG
9627-xxxxxx It's a 1996
It seems one of the most common problems are that,
half, or, all of the butterfly inside the carburetor breaks off.
and as you described, will cause a "no middle point" in RPM's,
and if your lucky, the broken piece of the butterfly may be wedged somewhere, (carb, intake port etc.) causing it to "shake",
Some people have not been so lucky... their butterfly was "gone"! (the engine ate it!)
Give the carb a good outside cleaning, remove, and inspect it, and
"IF" the butterfly is still intact,
take the carb apart while it's off the cart, and give it a good cleaning inside, and out!
Hope this helps, and let us know what you find!