Is it a requirement that you make your own inverter? Is that part of the project, or could you use a store bought one to get passed the initial electrical aspect and get to the mechanics? If you are just given batteries and need to get the AC, perhaps you could get one from the automotive or electronics section of a local store. They're relatively cheap, you can get one for $25-$35 that takes 12V DC (cigarette lighter plug) and outputs to a 120v AC outlet.
If you're actually wanting to build one yourself due to space or instructor requirements, then that wouldn't work. I also would be interested in how to make one.