Nowadays, billions of people use the Web in connection with their daily needs. A significant part of the needs are constituted by search tasks that are usually addressed by search engines. Thus, daily search needs result in regular user engagement with a search engine. User engagement with web sites and services was studied in various aspects, but there appear to be no studies of its regularity and periodicity. In this paper, we studied periodicity of the user engagement with a popular search engine through applying spectrum analysis to temporal sequences of different engagement metrics. We found periodicity patterns of user engagement and revealed classes of users whose periodicity patterns do not change over a long period of time. In addition, we used the spectrum series as metrics to evaluate search quality.