2004 xjr 200k. No faults.
Ok when the car is in park idles perfect everything smooth, when I put in to drive while brake engaged there is a strong vibration I feel. As I accelerate at low speeds and lower rpms like under 4 k and under 40 mph i feel vibration pretty heave while pressing the gas, it goes away once I take my foot off gas, or just coast like for instance stable speed, it's just the accel part that i feel a heavy vibration like somethings not right, if i floor it or WOT it feels like it's suppose to no weird vibrations. Could this be plugs, fuel filter?? THANKS

 

Is the check engine light on? It definitely sounds like an engine miss. If it is it should show a code on the OBD. If there is no light, there still may be a code caused by an intermittent fault.

So, I guess your first step is to check for a code, then we can go from there...