We introduce a Hamiltonian system which consists of two balls in the vertical line colliding elastically with each other and the floor. Wojtkowski proved that for the system of two linear balls with a linear potential (with gravity), there is a periodic orbit which becomes linearly stable if m1<m2 where m1 is the mass of a lower particle and m2 is that of an upper particle. For our system having a quadratic potential, we find an appropriate coordinate to obtain symplectic collision maps, obtain a periodic orbit and prove conclusively that the periodic orbit is linearly stable without the mass condition.