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late 14c., past participle adjective from break (v.). Broken record in reference to someone continually repeating the same thing is from 1944, in reference to scratches on records that cause the needle to jump back and repeat.
When Britain's Minister of State, Selwyn Lloyd[,] became bored with a speech by Russia's Andrei Vishinsky in UN debate, he borrowed a Dizzy Gillespie bebop expression and commented: "Dig that broken record." While most translators pondered the meaning, a man who takes English and puts it into Chinese gave this translation: "Recover the phonograph record which you have discarded." ["Jet," Oct. 15, 1953]