Dynamics of the shift in resonance frequencies in a triple pendulum

It is shown the solution of a triple pendulum in two dimensions with a harmonic perturbation using a nonlinear model. It is proposed a general matrix form for the model of pendulum with n-links.An analysis of resonance frequencies as well as dynamical states resulting from the variation ofmagnitude, frequency, and the friction among links is done. It has been found the pendulum can show periodic, quasi-periodic, and chaotic states. A comparison between results of the nonlinear model and its simplification for small oscillations is done. It is shown the analysis of the shift of resonances using transfer functions and numerical calculations