Chaotic dynamics of the two-body conservative system, which consists of a particle of massmbouncing elastically on a horizontal plate of massMsupported by an elastic spring, is investigated. The system integrates the properties of coupled oscillators with those of the bouncing-ball and impact oscillator problems. Results obtained by varying the mass ratioM/mand the spring constantkin numerical computations are presented in the form of time-dependent diagrams and discrete maps. The rich variety of resulting chaotic behavior includes strange attractors with fractal structure, resonant islands, crisis, and intermittency route to chaos. The system has a remarkable didactic value as an example of chaotic behavior in simple systems close to everyday experience. The integrable limitM=0is appropriate for introducing the phase portraits and discussing the interrelationship between the shape of the potential energy curves and the resulting oscillatory motion.