Good morning.
The noise you are describing sounds like a worn or bad motor mount allowing the engine to shift back and forth.
Below I posted the procedure for you as well as a couple of pictures. I also added the parts and a picture for you as well.
Roy
Removal Procedure
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1. Remove the coolant recovery tank mounting bolt.
2. Remove the coolant recovery tank and position it aside.
3. Remove the cruise control module mounting nuts and position aside.
4. Remove mounting nut from both A/C line (1) and position lines out of the way.
5. Install the J 28467-360 and raise the engine off of the mount.
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6. Remove the nuts holding the mount to the body.
7. Remove the bolts holding the engine mount to the bracket.
8. Remove the engine mount assembly.
part
https://www.rockauto.com/en/catalog/chevrolet,2002,cavalier,2.2l+l4+ohv,1434771,engine,motor+mount,5552
Images (Click to make bigger)
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Sunday, June 3rd, 2018 AT 5:48 AM