To clarify this is not a vibration. It is a surging by a "RUR RUR RUR RUR" noise, the car sways in rythm with this... Doesnt matter if cold start or the car has been running for a while... RPM in Park seems normal and unaffected by whatever issue is causing this, as does normal driving. When in Drive but stationary with the parking brake the car does not have this issue, same when in Reverse with the parking brake. However, when I switch the shifting knob to park the surging returns. Motor mounts or fuel injector issue?

 

I assume no codes, since you didn't mention it? While I am unsure the exact issue it could be, I think you can determine, or get further in diagnosis, if you have it in park and have someone give it some gas while you are watching the motor. It may move some, but bad motor mounts (to the point they are moving the vehicle) would show in the engine moving quite significantly compared to normal. In other words, if the motor mounts are bad enough to be causing the issue and moving the car. Revving the engine in park should produce evident movement on the motor.

If you are sitting in drive, but brake applied, and you hear and feel this, are the RPMs moving at all?

Interesting you mentioned this as today I was driving my X-Type to work and I had all the windows and sunroof closed because inexplicably in mid-August the temps were too cool to have them down, so I could hear a lot more of the car sounds and I had a similar sounds as I was rolling on the back country road at 65, but it is super weird because it can't be the engine, it can't be the tires as the slight whirring noise is about 1 time each second and I am running at like 2700K, so not my RPMs, and the wheels are surely spinning more than 1 time a second! Not super concerned about it for now but I was thinking "Well, that may be one of those I will never figure it out type of problems!"

 

here is a video. Going to check tonight to see if the engine is moving when power braking.

 

Second video