zanesen

1. rapt; enthralled; carried away
   Slušala ga je zanesena, bez ijedne reči. — She listened to him, enthralled, without a word.
2. (+ instr.) absorbed in; taken with
   Bio je potpuno zanesen svojim novim projektom. — He was completely absorbed in his new project.
   Zanesena muzikom, nije čula telefon. — Carried away by the music, she didn't hear the phone.
3. (of a person) dreamy; starry-eyed
   On je zanesen tip, stalno je u oblacima. — He's a dreamy type, always with his head in the clouds.

The object of enthusiasm is in the instrumental: zanesen muzikom.