a. Except as otherwise provided by law, the court shall have exclusive jurisdiction in all cases where it is charged that a juvenile has committed an act of delinquency and over all matters relating to a juvenile-family crisis. Upon the determination that a juvenile has committed an act of delinquency or that a juvenile-family crisis exists, the court may impose such disposition or dispositions over those persons subject to its jurisdiction consistent with the purposes of this act. Such jurisdiction shall extend in these matters over a juvenile and his parent, guardian or any family member found by the court to be contributing to a juvenile-family crisis. The court shall, in accordance with the Rules of Court, clearly specify the responsibilities of those subject to its jurisdiction with respect to the plan of rehabilitation for the juvenile.