Abstract: The swing is regarded as a variable length simple pendulum. Based on Gauss function，the velocity

of pendulum ball relative to pendulum rod is designed. When the swing moves with a large angle，it can meet the

requirements of “squatting down on the highest point and standing up on the lowest point”，because its parameters

are independent of swing motion. On this basis，the dynamic differential equation of swing is established，and the

motion of swing is simulated numerically，the motion process，work and energy transformation mechanism of swing

are obtained.

Key words: swing, parametric self-excited oscillation, mathematic model, numerical simulation