In the film when Aragorn rushes in the palace to announce that the beacons of Minas Tirith are lit, we see Theoden take a moment or two before deciding that Rohan would answer their call. I wonder is this scene in the book clearer, if it exists at all that is. Is Theoden hesitant?
In the text, Théoden offers to help basically immediately
The call for aid comes in a different form in the book, but more relevant to the question is the fact that Théoden almost immediately agrees to send in the troops (emphasis mine):
'Dark tidings,' said Théoden, 'yet not all unguessed. But say to Denethor that even if Rohan itself felt no peril, still we would come to his aid. But we have suffered much loss in our battles with Saruman the traitor, and we must still think of our frontier to the north and east, as his own tidings make clear. So great a power as the Dark Lord seems now to wield might well contain us in battle before the City and yet strike with great force across the River away beyond the Gate of Kings.
'But we will speak no longer counsels of prudence. We will come. The weapontake was set for the morrow. When all is ordered we will set out.
Return of the King Book V Chapter 3: "The Muster of Rohan"
Although he's rightfully concerned for his own borders, he doesn't express any of the hesitation he does in the film; he actually expresses quite a lot of hesitation in the movie, at one point outright refusing to come to Gondor's aid:
Gandalf: If the beacons of Gondor are lit, Rohan must be ready for war!
Théoden: Tell me. Why should we ride to the aid of those who did not come to ours? What do we owe Gondor?
The Return of the King (2003)