Harmonic oscillator mathematical model is a description of TEA CO2 laser vibrational dynamics, and it simplifies temperature model The equations are built using four characteristic variables for three vibration states of CO2 molecule and one of N2 molecule to show energy variety, to relate time to output intensity in cavity, light flux and gas temperature. The laser pulse waveform can be calculated with varied laser's parameters. The output power and energy can be obtained with intensity, it provides theoretical basis for laser design. Theoretical calculations shows a good agreement with the experimental result.