The children were running around the playground frenetically.

frenetically 是形容词 frenetic 的副词形式，frenetic 来自希腊语 phrenetikos（"疯狂的"），表示"极度兴奋的、狂热的"。frenetically 形容动作"疯狂地、极度兴奋地"进行的状态。