As others have said, it sounds like typical imbalance.
There are different externally weighted dampers, flywheels or converters for 318/340,360,and Magnum engines.
If either the damper or converter has been changed, they're suspects.
Mounts, bad plug wires or plug, or a cam going away could all also have a bit of a shake which worsens.
All of these can be checked or ruled out without the engine running. If something is wearing, running it is just risking catastrophic failure.
Inspect the mounts, pull the valve covers, check for loose pushrods at TDC of each cylinder, inspect plug wires and plugs (or replace if they're very old or show wear).
Pull the belts and look for loose bolts on any pullies or brackets then pull the damper and look for damage and to confirm whether it's the right configuration for your engine.
Next, try to get into the bellhousing area and see if there's a weight welded to the converter. If you search for images of stick converters, you'll see what it usually looks like.
Sharing pictures of all these things can also help plenty of the members here advise you.