Abstract: A dynamic rotation vector, including its starting point, length and phase change according to certain rules, is used to research the vibration of spring oscillator under sliding friction and air small damping. The vibration of spring oscillator is also studied under sliding friction and critical air damping （ or large air damping） , the curves of four kinds are given according to the initial value and damping. Four phase diagrams and phase diagram rotation vector of spring oscillator are analyzed.

Key words: spring oscillator, air damping, sliding friction, rotating vector