Not sure why people go down the harder path of investigation before the easier ones!
Get hold of the back of the exhaust and try to move it up and down, side to side. If its got a defective mounting rubber you will soon know.
If you are feeling really adventurous, lay on the ground and have a look. Again, any broken exhaust mount will be obvious, they tend to be simple O rings or other shaped rubber mouldings, figure of 8 or the like, from a simple bent piece of steel on the exhaiust to a similar one on the under-floor or chassis.