What you are describing is a tuned damper, all be it not a very well constructed one. Typically they need a sealed air space behind to work properly. Also more air space than a rug pad can provide. And you only ever want to use tuned dampers strategically, with a know issue at a specific frequency and a damper tuned at that frequency. Just throwing one together haphazardly will more likely just create a new problem where there wasn't one before.