You could put a capacitor across the sensor to "average" the oscillations. Better yet, a RC network tuned to give you the desired time you want.
I'm curious though, there is nothing in the datasheet says this will work as a "tilt" sensor. Only says it's a "vibration" sensor yet doesn't give you any specs on minimum movement required to trip the sensor. If someone moved the sensor very slowly would the sensor sense that? If not, it won't work as a tilt sensor as those trip when something is tilted no matter how slowly it's moved.
Bookmarks