I have a BMW 2000 323i that makes a vibrating noise

can you video it? could be many things could be a wheel bearing

may be you should make a diagnostic and you can do it in a garage or you can do it by yourself if you want to do it by yourself you need some tools and you can find some good ones here: spobd2.com

It sounds like your car is low on power steering fluid. When the power steering fluid is low, the power steering pump is running dry, which makes a grinding or moaning sound. Check the power steering fluid level and top up if necessary. It should be on the left side of the engine compartment. Your owners manual should have the exact location of the power steering reservoir, and what type of power steering fluid to use.
Good luck
Matt

Replace power steering rack and power steering pump. But first check fluid level. No fluid in reservoir can mimick same problem. Take off air box to adequately see level.

iam am no doubt totally wrong here ,but i would first of all check the power steering fluid level ,then turn steering from left to right with engine running and check the fluid level again

my 325i makes a whining type noise when driving (not all the time), but stops when I apply my brakes. Any idea what this is?

no filter, sounds like the steering rack is worn out and need to be rebuilt.

It might be a faulty power steering pump. Try checking the level of the power steering fluid. It is probably best you have your power steering system checked by a mechanic.

Does the noise occur only when the vehicle is moving?

Try moving the steering wheel from side to side, while stationary (but don't do it too often, or you might damage something). If the noise is still present when the car is stationary, then it probably is the power steering system.

If the noise only occurs while the vehicle is moving, it could be a problem with the differential/final drive, or even wheel bearings.

Hi these cars are known for the wishbone bushes failing and will cause the same symptoms as what you describe, there are 3 different bushes on the wishbone have them all checked for any play, Hope this helps

Is the belt on the power steering pump tight or loose does the pump makes a huming noise when turning steering all these are causes of hard to turn steering belt need to be (tight) on pump and pump must not be huming when turning steering add fluid if needed and play with steering to see if help if not need to replace pump