1997 Toyota Camry makes a vibrating sound near the Power...

It is difficult, if not impossible, to diagnose a sound or vibration without experiencing it firsthand. A loose belt will usually make a squealing sound. A belt that is too tight can ruin bearings on the power steering pump, alternator, AC compressor, and idler pulley and even damage the pulleys.

Check the fluid level in the power steering reservoir because if it is low, the pump can get noisy, especially when cold.

Other possible causes are bad or loose engine and/or transmission mounts.

I'm not sure if anyone will see my response here but I'll give it a try anyway...

I'm having the exact issue with my '90 Celica. I've been hearing this vibration noise whenever I come to start my car and after popping the hood, it seems to be coming from the power steering reservoir and/or pump. When I lightly push down on the cap of the power steering fluid reservoir, the vibration completely stops. I was thinking that something might be loose but I can't seem to find what it was.

Any ideas >

Try gently bending the ears on the power steering reservoir or cap so that the cap fits more tightly. Also look at the power steering hoses coming from the pump to make sure they are not coming in contact with anything.