At about 1030 Eastern time, the airplane was substantially damaged during a forced landing shortly after takeoff. The Private pilot was not injured; visual conditions prevailed. The pilot subsequently reported completing a preflight inspection and an engine run-up, both per the checklist, and noting no anomalies. After the takeoff, as the landing gear retracted, there was a loud noise and the engine began to vibrate severely. The pilot immediately checked the engine gauges and cycled the landing gear back to the down and locked position. The pilot elected to land straight ahead, and completed an emergency-landing checklist. The airplane came to rest approximately 500-700 feet beyond the departure end of the runway. Examination of the engine revealed that the number three cylinder had separated from the engine case. The piston and connecting rod were found in the forward section of the engine cowling, and the rod end cap was found on the runway.