3M Sound Damping Foil Tape

I have heard of people using tape like this...just be careful where you put inside your CD player...make sure the tape does not get too close to the tray which can sometimes get stuck on the tape.

I seriously doubt anything that thin and inexpensive is going to beneficially affect the resonant properties of your mdf shelving. That stuff is designed to dampen vibrations in metal air ducts, a completely different material and application. For damping the insides of components, get something designed for the job like this 3M material:

http://www.musicdirect.com/p-205-audio-additives-3m-damping-sheet.aspx

I have used material like this in cd players. If the cd player has inadequate damping and vibration control, it can (but might not) help to tighten the focus and resolution of playback.

There is a product called dynamat that I used when I was into car audio, 25 years ago, that would fit your needs. Dynamat is an excellent product and easy to work with. Good Luck.

I also use a product called Dynamat at home and in car audio, and similar products by other names, ( Blue Tac, U.S.C. ). A very useful butyl based product when used in the right application. Be a little cautious it's not easy to remove completely.