In this paper, the semi-analytical method of implicit discrete maps is employed to investigate the nonlinear dynamical behavior of a nonlinear spring pendulum. The implicit discrete maps are developed through the midpoint scheme of the corresponding differential equations of a nonlinear spring pendulum system. Using discrete mapping structures, different periodic motions are obtained for the bifurcation trees. With varying excitation amplitude, a bifurcation tree of period-1 motion to chaos is achieved through the bifurcation tree of period-1 to period-2 motions. The corresponding stability and bifurcations are studied through eigenvalue analysis. Finally, numerical illustrations of periodic motions are obtained numerically and analytically.

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