Ok so my car seems to shake a bit sometimes while driving. I started noticing it when accelerating. Doesn't do it all the time but just to try narrowing things down I coasted down a road in neutral and still had a bit of shake to it. I've noticed that the passenger side of the rear stabilizer bar has broken and it just hangs there. Could this be the cause, or something else?

 

Ok went for a long drive to get more data.. When slow accelerating, there is a shake which feels like it is right at the frame. Doesn't happen if I floor it. Most of the time it seems to roll without a problem but I do get a subtle shake at times.

 

Are all four of your wheels balanced? This is what I would check first. did you put a new or spare tire on and not get it balanced? Or could one of the counter weights fallen off? Check your rims....

 

Get your tires balanced and fix that stabilizerbar.

 

Tires are balanced. Had it done recently when a pot hole killed one of my tires.

Kinda narrowing things down, but my problem may in fact not be suspension related. Hard to tell sometimes but it may actually be the engine shaking it due to a miss (which would explain it happening rolling in neutral)