Answer:
The period of 1860-1914 would see the nationalist ideas become politically influential.
Explanation:
Nationalism as a political ideal was rationalized in the late XVIII century. With the French Revolution, the idea of an autocrat embedded with the will of the State was challenged by that of a State represented by its citizens, taking the idea from the old Roman Republic, but with the philosophical basis of the Enlightenment. Thus, between 1776-1815, nationalism was related to the notion of a citizen State against the monarchies, but not with the idea of territory and common language or history.
This would be dealt at the second period, 1860-1914. In Europe, this period would see the unification of Germany and Italy, while in the rest of the world (Asia, Latin America, the Middle East) saw the Meij Restoration in Japan, and the consolidation of the Latin American nations (the unification of Argentina, the struggle against French intervention in Mexico, the Triple Alliance war between Brazil, Uruguay, and Argentina, the Pacific War).
In this period nationalism become a key political factor, and in Europe, it would trigger the "armed peace" between the newly formed German Empire against France and Great Britain, that would lead to the creation of the Entente, the prelude to the Alliance that would enter the war against Germany in 1914. The aftermath of this period, that is the two World Wars, would see national extremism getting to power, and also the blending of nationalism with right-wing factions, that would emerge as fascism and nazism.
In the aftermath of 1945, and to 1960, nationalism would boom in the former European colonies in Africa and Asia, and prove to be a leading factor in the decolonization movements.
In can be concluded that nationalism was politically influential in the period 1860-1914, that it appealed to a commonality of language and history (this was also the Romanticism period culturally speaking) of the people, and that is consequences would be the World Wars, the breaking of the old empires of Austria-Hungary, Russia, Germany, and the Ottomans.