Nonlinear vibration of a pendulum with a support in harmonic motion

Abstract

The nonlinear vibration of a pendulum whose support undergoes arbitrary rectilinear harmonic motion is studied. The main attention is paid to the resonant cases and the stationary vibrations. The resonant conditions are explained. The amplitude-frequency curves are plotted for various values of parameters and the stability of vibration is investigated. The rotating motion of the pendulum and its stability are also considered.