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(-23) During cruise flight with the student under the hood the engine started to vibrate. The mags were checked but made the vibration worse. The oil gauges appeared normal. At this point the instructor could not maintain an altitude and selected a pasture to land. The a/c first touched down in a pasture on a heading of 030 degrees, 618 feet from where it came to rest on a heading of 010 degrees. After rolling for 36 feet the a/c became airborne for 60 feet and then settled back onto the pasture, rolling for 420 feet before heavy braking action took place. The heavy braking continued for abo ut 80 feet, which at this time the right main tire left the ground and cleared a corner fence post that was about 5 feet tall and about 10 inches in diameter. At this point the left wing tip hit the ground, damaging the plastic wing tip, the propellor also hit the ground at this time, bending one blade and nicking the leading edge of the other. As the right wheel rested back to the ground the right horizontal stablizer came down onto the corner fence post, damaging the horizontal. (.4) on March 24, 2000, at 1615 central standard time, a Cessna 172N airplane, N75958, was substantially damaged during a precautionary landing near Maud, Oklahoma. The airplane was registered to and operated by airman flight school, inc., of norman, Oklahoma. The flight instructor (CFI) and private pilot receiving instruction were not injured. Visual meteorological conditions prevailed and no flight plan was filed for the 14 code of federal regulations part 91 instructional flight. The local flight originated from the university of Oklahoma westheimer airport, norman, Oklahoma, at 1540. According to the CFI and private pilot, the flight departed on an "instrument training flight," during which the student was "practicing basic attitudes." They reported that during the flight the "airplane started to vibrate violently." They retarded the throttle and checked the magnetos; however, the vibration intensified. Subsequently, a precautionary landing was executed to an open field, where the airplane impacted a fence during the landing roll. According to an FAA inspector, who examined the airplane, the right horizontal stabilizer was bent upward and the propeller blades were damaged. He examined the Lycoming O-320-H2AD engine and determined that the #3 cylinder's exhaust rocker arm retaining stud had separated. A portion of the separated stud was found lodged beneath the intake rocker arm, and the remaining portion of the stud remained seated in the cylinder head assembly. The cylinder head assembly and the separated portion of the exhaust rocker arm retaining stud were sent to the Textron Lycoming materials laboratory, williamsport, Pennsylvania, for further examination. Macroscopic examination of the stud fracture surface revealed the presence of beach marks and ratchet marks on the fracture surface indicating that the stud failed in fatigue, which originated at the thread root from multiple origins. A hardness test reveled that the stud met the manufacturer's specifications and there were no additional defects noted with the stud's material. The airplane and engine underwent their most recent annual and 100-hour inspections, respectively, on February 8, 2000, at which time they had accumulated a total of 7,010.7 hours and 1,350.2 hours since overhaul, respectively.