I had a 3.5hp Snapper last week that would knock on start up and when the engine was slowing down, but not at full throttle or a steady RPM.
This is what I found inside.
It had a brand new blade when I found it and it started on the first pull and cut grass just fine. It was a mid 80's model Snapper HiVac. I changed out the rod, checked he crank, replaced the base gasket and mowed my lawn with it.
When I first started it, it sounded like a loose blade or engine.
I had a JD with a 6.75hp a few weeks ago that had a boom-a-rang shaped blade on it and a bent crank that not only was bent at the bottom, but it twisted below the rod journal putting the crank counterweights out of phase. I had straightened the lower crank, checked the key and put a new blade on it, it started hard but ran. It had a vibration but not that bad. I actually had cut my lawn a few times with it but it would stall easily and was hard to start when it got hot.
I tore it apart chasing the the vibration and found the bent crank. The lower half of the crank was twisted almost 1/4" putting the lower counterweight behind the upper weight about 1/4" .