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Merge two shapefiles in R, get a dataframe of variable value in each precinct

I’m not a GIS person, this is driving me nuts. I have a shp file of voting precincts. I have another shp file of radio broadcasts. I want to use R to geolocate the broadcasts into the precincts, so that I get a dataframe that records the signal strength in each precinct. This should be a basic merge but I am unfamiliar with GIS in R. Sorry for the basic question, really appreciate your help!!