This 2005 VW Jetta TDI came into the shop with a chirping noise from the belt and rattling noise from the engine. The belt had already been replaced and that helped the chirp but not the rattle. In this video I will show you how to test the alternator decoupler pulley sometime called an overrun clutch pulley and replace the pulley if it is bad. Replacement does require a couple of special tool which I will list below. Always remember to be safe while working under the hood and especially while near the belt system while the engine is running. Shut engine off and remove key from vehicle before starting the hands on testing and repair.

The VW special tool kit from AST https://amzn.to/2MBXzAF
The decoupler socket from Hazet https://amzn.to/2vDWIZT
Cheap version of the Hazet socket https://amzn.to/2P2n0gC
Basic decoupler tool kit https://amzn.to/2MEgYkP
Complete decoupler tool kit https://amzn.to/2P1VRKA

The above link are affiliate links and if you buy from the link then I will get a very small amount of support but it cost you nothing additional.