During an initial solo flight, the student pilot was conducting a series of three takeoff and landings. During the second landing, the airplane landed hard, bounced, and landed on the nose wheel landing gear, which resulted in the nose gear collapsing. Postaccident examination of the airplane revealed that the nose wheel landing gear was compressed upward and aft into the firewall and fuselage structure. The student pilot reported that at the time of the accident, no preexisting mechanical malfunctions or failures existed that would of precluded normal operation of the airplane.