...had a similar problem with my joystick, I use the throttle of the saitek x45 in combination with the Microsoft Sidewinder FFB2.
I had constant shaking like yours but no real ffb anymore, no resistance on stick. I unplugged the Sidewinder and replugged it again. The constant shaking was gone, now it doesent shake at all but I have a constant centering force and you have to press or pull against it. It gives you a better feeling for the aircraft. This shaking and bouncing on the stick makes no sense anyhow as long as you just sit in front of your pc. It only makes sense when you sit in a simulator cabin that shakes and bounces you arround.
Hope you get yours fixed.