Abstract
The spring-pendulum system has been of greet interest for a long time, and one tried to use the perturbation analysis to understand such a system. Until now, one cannot provide a satisfied result to explain the dynamics of the spring-pendulum system. In this paper, bifurcation trees of period-1 to period-2 motions in a periodically forced, nonlinear spring pendulum system are obtained through the discrete mapping method. The corresponding harmonic frequency-amplitude characteristics of period-1 to period-2 motions are presented, and the stability and bifurcations of period-1 to period-2 motions on the bifurcation trees are presented as well. From the analytical prediction, numerical illustrations of period-1 and period-2 motions are completed for comparison of numerical and analytical solutions. The results presented in this paper are totally different from the traditional perturbation analysis.
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