I have a 42" troy Bilt riding mower. I let someone use it a while back and now the deck vibrates very violent when blades are engaged. Could someone tell me something to check concerning this problem? Thanks a lot

Bent blade, bent shaft. Take the blades off, inspect and try to balance.
See the sticky at the top of the forum about blade sharpening and removal.

Check your belts for worn spots, and check the blades for warping. Also, it could be the bearings.