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In the context provided, the correct verb tense to use is "had been". The sentence would read: "The history teacher showed her students footage taken from wartime newsreels. The films gave them a vivid sense of what it had been like at the time."
This is because "had been" is used to indicate an action or state that occurred in the past before another past action, which fits the situation where the students watched the newsreels after the events depicted had already taken place in the past.