Used for pg. 75

A Fourier series is a way to expand a periodic function in terms of sines and cosines. The Fourier series is named after Joseph Fourier, who introduced the series as he solved for a mathematical way to describe how heat transfers in a metal plate.

The GIFs above show the 8-term Fourier series approximations of the square wave and the sawtooth wave.

Simulation der Umlaufbahn der Erde um die Sonne

Potential energy to Velocity

Problem of the sliding chain

Spring-Mass model used in IACS physics class

Rotating Pendulum Z201 from System Zoo 1 p80-83

Problem of the sliding chain

Simulation der Umlaufbahn der Erde um die Sonne

Tischtennisball aus 5m Höhe mit und ohne Strömungswiderstand.

Problem of the sliding chain

Problem of the sliding chain

Bipolar II treatment modeling using Van der Pol-like oscillators.

In this simulation an afflicted individual with Bipolar II disorder is put to treatment after 20 months the calibration of the medicine or treatment he recieves is such that it simulates the natural cycles of a "normal being". You can note by manipulating the parameters that sometimes too much treatment disrupts equilibria. Also note that in the state diagrams there are 2 limit cycles, the lower one being the healthiest as there are less changes.

This system models the equation of motion of a projectile in the horizontal (x) and vertical (y) directions, with a linear drag force. The drag is quantified by a drag coefficient C, which can be set by means of a slider.

A PID control loop for a simple linear system

Problem of the sliding chain

Simulation der Umlaufbahn der Erde um die Sonne

Le but de cette simulation est de montrer comment on peut implémenter de manière hydraulique les différentes portes logiques (à 2 entrées)  susceptibles d'être utilisées pour construire des circuits logiques.