On July 30, 1994, at 1100 Pacific daylight time, a Cessna 172N, N739RF, sustained substantial damage during a hard landing at Cameron Park, California. The aircraft was owned and operated by Patterson Aviation, Inc., and was rented by the pilot for a local area personal flight. Visual meteorological conditions were prevalent at the time and no flight plan had been filed. The certificated private pilot was not injured. The flight originated from the Sacramento Executive airport, Sacramento, California, at 0915 on the day of the accident. The pilot reported that he was making a visual approach to runway 31 at Cameron Airpark. He stated that he came in high over the runway numbers with full flaps. He maintained his descent attitude until he judged his position to be about 10 to 15 feet above the runway, and then began to flare and reduce his airspeed. As the aircraft was about to touch down, he stated that he inexplicably pushed forward on the control wheel to get the aircraft on the ground. He did not know why he performed that action since he does not normally attempt to land in that manner. After the initial touchdown, the aircraft bounced back into the air. At this time, he felt he could recover and continue the landing sequence, so he again attempted to flare the aircraft over the remaining runway. He said he may have misjudged his altitude on the second attempt and the aircraft bounced about 10 or 15 feet in the air. After the second bounced landing, he felt that he did not have sufficient power and runway remaining to attempt a go-around. He continued to make a third attempt, and the aircraft remained on the runway after touchdown. The pilot reported that after turning off the runway onto the taxiway, the aircraft became difficult to taxi. He attributed the difficulty to the fact that his destination on the airport required him to taxi uphill. An inspection of the aircraft by the owner/operator revealed that the nosewheel tire was blown, the nosewheel strut was broken at the top attachment point, and the engine firewall was buckled.