At 2256:33 local, approximately 90 seconds after takeoff, the cockpit voice recorder heard the automated voice announce “altitude” as the aircraft was approaching it’s 2,000 foot restriction. The airplane’s initial climb rate at that point however, exceeded 6,000 fpm and a second altitude warning was heard 14 seconds later as the aircraft passed through 2,000 feet. The CJ4’s bank angle increased to about 62 degrees and the pitch attitude decreased to about 15 degrees nose down, as the airplane continued through the assigned heading. The bank angle ultimately decreased to about 25 degrees. During the subsequent dive, airspeed and descent rate reached about 300 knots and 6,000 fpm, respectively. The enhanced ground proximity warning system provided both "bank angle" and "sink rate" alerts.