The student pilot was approaching to land at his home airport on a solo flight. The wind was almost directly down the runway at 6 knots. After he turned onto the base leg of the traffic pattern, air traffic control (ATC) inquired if he had turned base. He informed them he had and needed to immediately turn on the final. ATC then asked an airplane to hold position. His approach angle was normal, he was on the centerline, and his airspeed was about 85 mph. As he crossed the threshold of the runway, he reduced the throttle to idle, and the airplane touched down firmly, but did not bounce. When the nosewheel contacted the runway pavement, the airplane began shaking and the airplane began heading towards the right side of the runway. The student pilot attempted to correct, but his corrections started a series of oscillations which grew in amplitude. The airplane then entered the grass next to the runway and he let the airplane continue along its path of travel for fear of flipping the airplane over. The airplane then encountered a drainage ditch and came to rest on the other side of it. The airplane was substantially damaged. The pilot reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation.