buck up vs light a fire under

buck up

verb
  • To become encouraged, reinvigorated, or cheerful; to summon one's courage or spirits; to pluck up courage. 

  • To pass on to higher authority for resolution. See also pass the buck. 

  • To encourage; to hearten. 

intj
  • Cheer up; take courage; take heart. 

light a fire under

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

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