Parametric resonance induced chaos in magnetic damped driven pendulum

• A damped magnetic pendulum is considered driven by off resonant magnetic field.
• Our system is chaotic only when the conditions for parametric resonance are fulfilled.
• Conducted experiments give a good agreement with theory and numerical simulations.
• Calculated Lyapunov exponents are compared with parametric instability growth rates.

A damped driven pendulum with a magnetic driving force, appearing from a solenoid, where ac current flows is considered. The solenoid acts on the magnet, which is located at a free end of the pendulum. In this system the existence and interrelation of chaos and parametric resonance is theoretically examined. Derived analytical results are supported by numerical simulations and conducted experiments.