Shoot the metal plates with arrows (I used bolts), and you will notice that a function will happen with each one such as a bridge doping, gate opening. It just takes time to fiddle with it so you can get an idea of what to expect in a order.
http://www.uesp.net/wiki/Skyrim:Dead_Drop_Falls is the UESP wiki on Dead Drop Falls, as well as a https://www.youtube.com/watch?v=8YRtaXW4j5g of it, unless you don't want to be spoiled on how things work!

Like I said, I used bolts so I do not know if regular arrows will do it (But I am sure it does).
I think there are traps that activate as well so watch for that!