In one aspect of the invention, a method for drilling a bore hole includes the steps of deploying a drill bit attached to a drill string in a well bore, the drill bit having an axial jack element with a distal end protruding beyond a working face of the drill bit; engaging the distal end of the jack element against the formation such that the formation applies a reaction force on the jack element while the drill string rotates; and applying a force on the jack element that opposes the reaction force such that the jack element vibrates and imposes a resonant frequency into the formation.