I have had a 2005 Roadster for the past 10 years. A month ago I heard an odd metallic rattling sound under the hood. Looking under the hood, I saw a part that was obviously broken. I didn't know what the part was, but it didn't affect the engine performance. So, I got some wire and tired it up out of the way so that it wouldn't hit anything else in the engine compartment.
More recently I had problems with my idler pulley and had to replace it. After removing the coolant fan and replacing the idler pulley, I snapped a couple of good pics of the broken "rattling" part. It is highlighted in yellow in the pictures below.
Can someone identify for me what this is and how I can replace it?

 

I believe they only used the dampener on manual transmission cars. The automatics don't have it.

 

My 2004 6 speed had one, I thought they dispensed with altogether after a while, you could be right though as jerky take offs may make the belt jump off a pulley.
My 2005 auto does not have one.
Frankly after having it not work after this time maybe it could be left off altogether.How many miles on that car?

 

We've had two 04 autos and two 05 autos. None had the dampner.