2010 Ford F-150 4.6 rough idle (extra rough when a/c is on) after throttle body cleaned

Purge valve solenoid (new) throttle body cleaned. What could this vibration (constant in and out) be? The engine itself shakes along with the exhaust. I can feel the vibration more while the doors are open.

You may have accidentally 'bumped' something. Check the vacuum hoses, spark plug wires, sensor connectors, etc.

Check that you don't have any air leaks. I believe they have a mass air flow sensor. If there's any air leaks like a cracked intake duct it'll run rough.

Check that you don't have any air leaks.