The phrase "short, sharp shock" means "a quick, severe punishment." It is an example of alliteration. Although the phrase originated earlier, it was popularised in Gilbert and Sullivan's 1885 comic opera The Mikado, where it appears in the song near the end of Act I, "I Am So Proud". It has since been used in popular songs, song titles, literature, as well as in general speech.
John Conington's 1870 translation of the First Satire of Horace includes the following lines:
In Act I of the 1885 Gilbert and Sullivan opera The Mikado, the Emperor of Japan, having learned that the town of Titipu is behind on its quota of executions, has decreed that at least one resident of the town must be executed immediately. Otherwise the town will be reduced to the status of a village. In the dialogue preceding the song, three characters, Pooh-Bah, Ko-Ko and Pish-Tush, discuss which of them should be beheaded in order to save the town from "irretrievable ruin". Although Pooh-Bah's enormous "family pride" would normally prompt him to volunteer for important civic duties, he has decided to "mortify" his pride, and so he declines this undertaking. He points out that since Ko-Ko is already under sentence of death for the capital crime of flirting, Ko-Ko is the obvious choice to be beheaded. Pish-Tush helpfully notes that he had heard that beheading is not all that painful (although he does not seem certain of this).
The three characters then sing the song "I Am So Proud". In the last lines of the song, Pooh-Bah, Ko-Ko and Pish-Tush contemplate "the sensation" of a "short, sharp shock" caused by being beheaded:
The phrase is particularly popular in music. For example, the phrase is used in the song "Us and Them" (from Pink Floyd's 1973 album, The Dark Side of the Moon).
Short Sharp Shock is also the name of a 1984 album by Chaos UK. It also appears in the title of an album, Short Sharp Shocked, by Michelle Shocked and the EP "Shortsharpshock" by Therapy?. Short Sharp Shock is the name of a crossover thrash band from Liverpool, England. The phrase is used in the song "East Side Beat" by The Toasters, and in the 1980 song Stand Down Margaret by The Beat. It can also be found in the lyrics of a Billy Bragg song entitled "It Says Here" found on his 1984 album Brewing Up with Billy Bragg and of a They Might Be Giants song entitled "Circular Karate Chop" on their 2013 album Nanobots.