Engine vibration and check engine light turns on

That description is textbook for a misfire. The first step would be to get it scanned and see what code(s) it has. I would expect a P030X with the X being the cylinder that is misfiring. First question will be which engine it has, most common is the 3.7 V6. That engine has a few known issues when it comes to misfires. The spark plugs (NGK (6987) ZFR6F-11G) need to be changed out every 30,000 miles or so, don't bother trying to install anything fancy like a platinum or other exotic plug, every 3.7 I've dealt with has misfire issues when those were used, and the miss went away when the plain copper style plugs were put back in. If those haven't been changed they are the first item to check. Next would be the coils, to test those you would start with the scan to find out what cylinder is the issue. For this lets say it is #3 that is the problem. So a code P0303, Erase the codes then remove the coils from cylinder #3 and cylinder #1 look over the #3 coil for any damage or carbon tracking or other issues, if nothing is obvious swap the coils between the two. Now run the truck and see if it sets a code again (it likely will) then scan it. If the code still shows as #3 then you know to look farther, if the code is now showing P0301 then the coil needs to be replaced, If that is the case I try to use OEM coils, they seem to have the least problems. Next would be to check the fuel injector for that cylinder, that can be done the same way as testing the coil.
If the code still stays in cylinder #3 then there are more steps to take, the 3.7 has a few known issues that are deeper in the engine, like the rocker arm coming off for a cylinder, not likely in this case as it would miss all the time and run rough as well, the next is the valve seats get loose, this is possible but not as likely as a bad plug or coil as they are the biggest issues.

Thank you expert Steve. It's amazing how much help is out there. I highly appreciate all you have explained and I'll get to work on this immediately.

Please keep us informed on what you find or if you need more information.