Experimental and numerical investigations are carried out on an autoparametric system consisting of a composite pendulum attached to a harmonically base excited mass-spring subsystem. The dynamic behavior of such a mechanical system is governed by a set of coupled nonlinear equations with periodic parameters. Particular attention is paid to the dynamic behavior of the pendulum. The instability threshold of the pendulum is determined from the semi-trivial solution of the linearized equations. The set of nonlinear differential equations is then integrated with respect to time using step-by-step methods. The developed experimental setup makes it possible to analyze the angular displacement of the pendulum using an opto-electronic sensor. The motion of the pendulum is numerically analyzed via phase-plane portraits and Poincaré maps. A subcritical bifurcation is plotted and chaos is observed. The predicted results are experimentally validated.