ABSTRACT: The oscillations of a pendulum suspended on an elastic beam are examined. The mathematical pendulum is a material point suspended on an ideal rigid and massless rod. The upper end of the rod is connected by a joint with an elastic beam on two supports. The beam is considered to be perfectly elastic and massless. The system has two degrees of freedom. The nonlinearity is due only to a geometric nature. A nonlinear system of two differential equations is derived. A numerical solution was made with the mathematical package MatLab. The laws of motion, generalized velocities, generalized accelerations, and phase trajectories are obtained. The internal force in the rod as a time function is also determined. The dynamical coefficient for the rod is calculated. In order to continue the task by preparing an actual model and conducting experimental research, the projections of the velocity and acceleration of the material point along the horizontal and vertical axes, as well as their magnitudes, are determined. The obtained results are presented graphically and analyzed in detail. The research has a theoretical and applied character.
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