Theoretical and experimental study of a parametric resonance simple pendulum
A parametrically driven simple pendulum was constructed so as to introduce the experi-mental education of basic physics.The movement near the equilibrium position was studied both in theory and experiment.By using first-order perturbation method,the general expression of the mo-tion orbits was obtained theoretically,based on which the boundary of parametric resonance zone was determined and the dependence of orbital characteristics upon the driven parameters(frequency and amplitude)were derived.In experiment,a two-dimensional displacement sensor was built by using two one-dimensional laser displacement sensors,by which the trajectory of the pendulum was meas-ured in real time.Within the parametric resonance zone,the orbital divergence exponent and a proper-ly defined phase difference between the pendulum and the driven signal were measured at different driving frequencies.At the center of the resonance zone,the relationship between the orbital diver-gence exponent and the driving amplitude was measured.At the edge of the resonance zone,the de-pendences of beat frequency and depth of modulation of the envelope of orbit on the driving frequencies were measured.All the measurement results were in good agreement with first-order perturbation cal-culations.
万方数据
维普
