I’m currently a Sophmore Mechanical Engineering student who wants to start participating in undergrad research. However, I don’t know who would be the best person to contact for research opportunities. The engineering website says to contact Dr. Midkiff for undergrad research opportunities in MechE, but I also got an e-mail over the summer saying I was assigned to Dr. Bittle as a faculty mentor. That e-mail said that you can talk to your faculty mentor about co-op choices, research opportunities, etc.
I’m most interested in researching dynamic systems and controls, which are Dr. Mahmoodi and Dr. Yoon’s research interests, however their webpages don’t mention undergraduate research opportunities, only graduate.
Right now, I’m not sure if I should contact Dr. Midkiff, my assigned faculty mentor Dr. Bittle, or the professor I’m most interested in doing research for. If any other current or past engineering students who the best person to contact for undergrad research, I would love your advice 
Contact your assigned faculty mentor first and let him refer you as is appropriate.
I think contacting any or all of them would be fine. My daughter isn’t an engineering major, nor does she have an assigned advisor or faculty mentor, but when she was looking for her first CBH research project, she contacted the head of her department as well as a couple professors. The department head met with her, but it was one of the professors she contacted directly that gave her the project. The other prof contacted her with a project the following year.
Talk to both of them about research, but talk to your mentor regularly. If you are considering coop, research, adding a minor, etc, email your concerns or questions to your mentor, just make sure you can’t already find the answers via Google (your mentor does have better stuff to do). What would be really helpful is scheduling an appt with your mentor and just talking with them about your plans for the future. In person talking can be really wonderful, and it will also make you more memorable to your mentor, who could possibly give you recommendations in the future.