what would make my 2010 pt cruiser vibration at idle and in reverse

I'd check and clean anything that has to do with idle air system. I' clean the throttle bore and around throttle plate. Clean any small passages in throttle body. Check and clean iac/idle air control. I don't believe you have etc/electronic throttle control on this vehicle. Any applicable trouble codes? Just my opinion.

Check the bolts on the Radiator bracket if some are missing the radiator will cause a vibration, it will increase when fan is on witn A/C use