encourage vs light a fire under

encourage

verb
  • To mentally support; to motivate, give courage, hope or spirit. 

  • To spur on, strongly recommend. 

  • To foster, give help or patronage 

light a fire under

verb
  • To motivate or encourage (someone) to start sooner or move faster. 

How often have the words encourage and light a fire under occurred in a corpus of books? (source: Google Ngram Viewer )