Heretic of The Seventh Circle
Eomer definitely went into a frenzy. There’s really no other interpretation of that scene, especially if you’re interpreting Theoden’s scene that way.The quote I gave was from the moment of the charge.
"Suddenly the king cried to Snowmane and the horse sprang away. Behind him his banner blew in the wind, white horse upon a field of green, but he outpaced it. After him thundered the knights of his house, but he was ever before them. Éomer rode there, the white horsetail on his helm floating in his speed, and the front of the first éored roared like a breaker foaming to the shore, but Théoden could not be overtaken. Fey he seemed, or the battle-fury of his fathers ran like new fire in his veins, and he was borne up on Snowmane like a god of old, even as Oromë the Great in the battle of the Valar when the world was young."
The battle-fury thing is pretty clearly about Theoden in this passage.
And, Eomer does get a similar moment, but the description isn't quite as explicit - he could just be really freaking mad. And this happens late in the battle, which would seem odd for the barbarian type, who usually leads with RRRRarrghhhghh!, so I didn't mention it. And if we are going to interpret everyone who ever gets angry in battle as a barbarian... that's a lot of barbarians.
That said, Eomer is of the same bloodline. If you wanna call him berzerk, feel free.
As for the lateness of the scene in the battle, that’s a rather odd argument. Most berserkers I’ve read hold out on that state until things are dire. I can’t think of any who start battles in that state, except for actual D&D characters.