2004 Toyota Camry Car shakes after 1 hour drive

I live in Kansas City and my son attends college at St Louis. Two weeks ago he drove his car home without any problem. But when he back to St Louis, after one hour on the highway, the Camry starts to shake up and down a lots and sometimes swing left to right or right to left and hard to control the steeling wheel. He manage to drive to St. Louis. After off the highway, the Camry continue shaking. Even when he stopped, the Camry still continue shaking. But, the next two weeks, he drive the car around the campus without any problem. Before the Thanksgiving, he drove the Camry from St. Louis back to Kansas City, after one hour, the Camry started shaking up and down again. He manage to drive the Camry home with some difficulty. He arrived home midnight, so I didn't have chance to test it. I test drive it around the next day on the highway for nearly one hour but the car stays quiet and smooth. Today, for the whole day, I drive it around shopping to many stores, sometimes on the highway for more than half hour, but the car remains stable and smooth.