The results of numerical and real experiments with the mechatronics set-up are desribed. The experimental mechatronics set-up consists of single and coupled double pendulum-like electromechanical system connected to the personal computer. The mathematical models of mechanical and electromagnetic processes in the system, data exchange interface and software for laboratory experiments are described. The analysis and control design problems for the system are difficult because only period of oscillations is available for online measurement and only pulse control torque can be applied. The algorithms for typical analysis and design problems (swinging and parameter estimation) are presented and studied both numerically and experimentally. Pulse-width modulated algorithm with the time shift for swinging the pendulums is described. The results of the paper lead to better understanding features of the excitability index - new characteristics of resonance properties of nonlinear dynamical systems.