Our everyday language is regulated by the cultural context, and also by cognitive features such as imitation and limited memory. Here we study how these factors interact to produce the dynamics of word usage. We capitalized on previous research showing that the occurrence frequency of words presents regular oscillations mounted on slowly drifting levels. We associated the drifting with the cultural environment and used it to drive a simple mathematical model that fits the data, capturing the dynamics of word usage in terms of imitation and memory. Fitting the dynamics of thousands of words across the last three centuries, we show that the oscillations are near to self-sustained and that the usage of a word at a given time is mainly influenced by its usage 7 years earlier. We found that words with similar usage form groups that represent keywords of historical periods. Finally, with the aid of our model, we show that the oscillatory coherence observed within these groups is provided by the cultural context driving the memory of the words. These results contribute to unravel how human cognition and historical forces interact to shape our use of language.