I have a Standard Horizon wind instrument and have the same problem with oscillation. I've tried the service route to no avail. I believe that the system I currently have is just cheap because the more advanced systems have "damping" or "dynamic damping" which will reduce or eliminate the oscillations primarily caused by the bouncing of the mast.
I have since ordered the B&G H-1000 system which has damping built in to it. I presume it will be more accurate as well. But the biggest reason I'm switching is that I want more detailed information for racing -- specifically True Wind Direction. I'm ordering extra displays to accommodate the increased data that we can use on a consistent basis.
I know this isn't a fix, but I found a need to scrap our current system and go with something better. Just in case anyone wants to know the cost, I ordered the H-1000 system which comes with one display, the wind, speed and depth sensors, a flux gate compass, the electronics and NMEA interface, along with an analog wind angle display and a triple digital display for almost exactly $3,000 from P-yacht. This is about $1,000 savings over retail.
Jim McCone
Voice of Reason E-32-2, hull #134