1998 different kind of AC problem

When I turn the AC on, I get a strange kind of rattling/shaking noise from under the hood. My wife commented it almost sounded like the car was purring. I can't exactly pinpoint where it's coming from, but I can't hear it with the AC off. Any ideas on what it might be?

Might be the AC compressor clutch, could be sticking.

How would I check that? I'm trying to do as many repairs myself as possible. This thing keeps breaking down and I'm tired of paying to have a mechanic fix everything. I think I'm already stuck having the front suspension replaced. I think it's missing some brearings. The more I can do myself, the better.

Thanks for your help!