If your engine vibrates at low rpm but seems smooth at higher RPM, then you may have a worn engine mount. The mounts have large chunks of rubber in them that absorb the vibrations. Apparently, they wear out fairly quickly, in about 5 years or so, is what I was told. It is apparently a common problem. If it is anything like my 93 Saturn, it is the upper engine mount, and it is relatively easy to replace. Ask a Saturn dealer for a quote, or if you are mechanically inclined, you can buy the mount and install yourself, working from a Haynes manual. A place to check for advice is Automotiveforums.com. Lots of helpful information and answers to lots of questions.
Low pressure in the tires can cause shaking, the alignment can cause shaking also.
check your engine mounts..I am not sure where they are but if you can move the engine with a prybar you need new mounts..they arent to expensive
There is no external timing marks on 2001 Saturn.
The upper engine mount is collapsed. On the passenger side by the coolant reservoir look at the mount If you see 1/4 inch or more gap the mount is collapsed and will cause the whole car to vibrate
check cv axles, transmission, and tires.
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