On October 18, 2018, about 1057 eastern daylight time, a Cessna 172S, N924MM, was substantially damaged following a partial loss of engine power and forced landing after takeoff from Lynchburg Regional Airport (LYH), Lynchburg, Virginia. The flight instructor and the student pilot were not injured. The airplane was operated by Liberty University under the provisions of Title14 Code of Federal Regulations part 91 as an instructional flight. Visual meteorological conditions prevailed, and no flight plan was filed for the local flight that was originating at the time of the accident. The flight instructor, who was in the right cockpit seat, reported that ground operations were normal, including pretakeoff engine indications. The student performed the takeoff on runway 4. After flap retraction, about 200 feet above the ground, they observed an engine vibration and the airplane shuddered. They noted a decrease in engine RPM with degraded performance. The flight instructor took the controls and noted that the airspeed had dropped to just above stall speed and the stall warning horn sounded. He lowered the airplane's nose to prevent a stall and attempted to land on the intersecting runway 35. The airplane touched down with about 100 feet of runway remaining. Realizing that he could not stop the airplane within the remaining runway, the instructor steered the airplane to the right to avoid a steep drop-off under the extended centerline of the runway. The airplane departed the runway surface, collided with a drainage ditch, and came to a stop in the grass in a nose down position. The pilots egressed the airplane and were met by first responders. A Federal Aviation Administration inspector responded to the accident site and examined the wreckage. He reported that the outboard portion of the left wing sustained structural damage during the landing. The propeller struck the ground during the event.The inspector examined the engine after the recovery of the wreckage. A cylinder pressure/leak check (with 80 psi input pressure) was performed. The Nos. 1, 3, and 4 cylinder readings were 74, 74, and 78 psi, respectively. The No. 2 cylinder read 22 psi. The No. 2 cylinder spark plugs were oil soaked. The No. 2 exhaust valve was stuck open; air could be heard escaping past the valve. There were no cracks or leaks observed in the cylinder body. The engine had accumulated 2,106 hours since overhaul, and the manufacturer's overhaul interval on the engine was 2,200 hours.