Exercices

In this section, we propose quick exercises that can typically be done in an hour and a half.:

• Simple pendulum (duration: 1.5 h): introductory exercise that proposes to model a simple pendulum and to put into practice the notions available in the course. The oscillatory or non-oscillatory form of the solutions will be discussed and the phase plane will be used to better understand these differences.

• Driven Harmonic Oscillator (duration: 1.5 h): In this introductory exercise, you will put into practice the notions seen in class in the case of a driven harmonic oscillator. The presence of a damping and an excitation leads to the presence of a unique orbit which is different from the case of the simple pendulum.

Practical work

In this section, we propose longer exercises that can be done without assistance, typically in 4 hours.

• Vibrational energy harvesting using a Duffing oscillator (duration: 4 h): The Duffing oscillator is a non-linear oscillator due to its position-dependent stiffness. It is one of the simplest oscillators capable of exhibiting chaos. In this exercise, you will be led to think about the notions of orbit, sub harmonic, chaos and Poincaré section.