My car makes this sound.... or this vibration.... What is causing it??

Noises, vibrations, and most transmission problems must be experienced, first hand, usually, in order to get an accurate diagnosis. Vibrations, and noises can be caused by any number of problems, and I have seldom seen any duplicate causes; I have to treat each case individually, test driving the vehicle, testing to see when the noise, or vibration happens and when it does not. I check to see the frequency of the vibration or noise, to determine where the cause may be. If the vibration is at wheel speed, then I can assume that it cannot be caused by the engine, transmission, or driveshaft, as these usually turn at around 3 or four times wheel speed. If the vibration happens while racing the engine, sitting still, then I can assume that the noise, or vibration must be engine/engine accessory-related, or torque converter/flywheel/clutch-related. The point is, these noises/vibrations can rarely, if ever, be solved over the internet or on the phone; you must take the vehicle to a reputable repair shop and have them listen, drive, and diagnose the problem properly. I often remove the serpentine belt (or fan belt, on an older vehicle) for a short while (only a few minutes, so you will not overheat the engine) and try to duplicate the vibration or noise; if the noise is alternator or water pump, the noise will go away using this techinique. I have been known to remove the transmission, and torque converter and start the engine to further eliminate a possible torque converter vibration.
Many vibrations, and noises, can be blamed on bad engine/transmission mounts. With bad mounts, the rubber, designed to isolate normal vibration/noise, insulating it from the driver. If the rubber has deteriorated, the mount can no longer isolate the engine/transmission/rearend noises and the result is an annoying noise or vibration.
It is all trial and error, and there are no "normal problems"; just unique problems that your vehicle has that need careful attention. Trust me.... if your mechanic cannot fix it, while working with the vehicle first-hand, then I surely will not be able to tell you where the problem lies. I have no crystal ball; I just check out the car, first hand, and try to duplicate the noise, or vibration, while eliminating the suspected cause/causes of the problem.