The investigation of a physical pendulum motion, which move along a horizontal axis

Abstract

The article presents a study of the physical pendulum, taking into account the force of friction in the kinematic pair, as a result of which oscillations are damped. Graphs of the dependence of the pendulum deflection angle α and the angular velocity on time for different values of the velocity v have been given. It has been established that the speed of the sleeve significantly reduces the amplitude and angular velocity of the pendulum, and the frequency of its oscillations does not depend on the presence of dry friction in the system. The dependences of the change in the amplitude of pendulum oscillations have been given and the results of numerical integration of the differential equation of pendulum motion have been obtained. The graphical dependences of the pendulum deflection angle and the movement of the sleeve x along the horizontal axis from time to time have been obtained at different values of the coefficient of friction. It has been found that during the first five seconds of the system movement, the axial speed of the sleeve is practically independent of the coefficient of friction (at f = 0.3… 0.5). To verify the obtained results, an experimental laboratory installation has been designed and manufactured. Theoretical studies are satisfactorily consistent with experimental data, with an error not exceeding 16%. The obtained dependencies can be used in the design and study of various mechanisms, the motion of which is described by similar differential equations. Such mechanisms include inertial conveyors, the gutter of which performs in addition to longitudinal and transverse oscillations. In addition, the proposed technique can be used in the study of the motion of bulk materials in an inclined cylinder, which performs torsional oscillations around the axis of symmetry.