1995 850 noise under hood with and without running engine
 

This is a 1995 850 with more than 170k miles. I've been driven it for about 10 years.

What I notice is some noises under the hood.

Without starting the engine, I can hear the following sound.
I feel it comes from someplace at the passenger side. But not sure where exactly it is.

After starting the engine, besides the above noise, I can hear a louder noise with less frequency and I can see the engine is shaking a little bit.

I have no idea about the first noise. About the second noise, I found some posts and it looks like it may be caused by the serpentine belt idler pulley. Any suggestion about the causes of the noises and how to repair them? Thanks a lot!

I think that the first video/audio is a vacuum pump designed to keep the power brake booster fully loaded. That's the first thing that came to mind. I can't think of anything else that would run with the key on that would make that kind of sound. Definitely the bearings on the way out.

The second sounds like the plastic pulley on the tensioner. They are easy to change and I've done a bunch of them.

If the car has headlight wiper motors, unplug them first.

Yeah. That seems high pitched for the headlight wiper motor, but that is where you start. Once they quit working, they don't know how to get back to park.

Thanks a lot for all your advice.

The first noise turns out to be the motor for headlight wiper. Somehow it gets stuck. I'm not sure whether I'm going to fix it or just disconnect it. I don't fell the headlight wipers very useful. Actually, the driver side one has missed the wiper for years.