Abstract: The motion equations of a spring-spiral-pendulum system are derived by using the Newton＇s second law.The equations are a set of nonlinear ordinary differential equations which indicate that there exist complex dynamical structures in a spring-spiral-pendulum system.Theoretical analysis shows that there exists an internal resonance phenomenon,which is verified by the numerical results,when the system of spring-spiral-pendulum vibrating is freely.For the general case,we believe that the motion of a vibrating freely spring-spiral-pendulum is probably semi-periodic.

Key words: spring-spiral-pendulum, nonlinear vibration, internal resonance