Abstract: The autoparametric resonance of three-dimensional spring pendulum is analyzed in terms of both the theory and the numeral calculation. It is found that the motion of three-dimensional spring pendulum in the horizon- tal plane can be approximated as the line segment with continuous deflection. The polar angle of the spring pendu- lum in the horizontal plane remains approximately constant within a period of time. In the case of micro-vibration the relation between the change of polar angle and the initial conditions is linear.

Key words: three-dimensional spring pendulum, MATLAB, autoparametric resonance