senior project 1

Define carefully, and then formally prove or disprove 'reciprocity'.

Find a local small company that has might like free work.
It would be good if you had a friend at these companies to break the ice,companies would be skeptical about someone just walking in and offering free work. Let this company know what facilities your school has for you to use. Find out what the company makes, submit a list of things you can do for them. Many small companies don't have the expensive equipment that a college has. My company teams with UC Santa Barbara a lot for high frequency testing.

This company may have a product that needs to be optimized and would like to have someone analyze it, redesign it and provide them alot of free redesign. Or find a cheaper way to manufacture the same device, or cheaper testing. If you do a good job, they'll probably pay you something too.
Most beginning engineers take previous work at a company and improve it/change it, as opposed to inventing new technologies.
good luck,
kch