Collection of Exercises

Interdisciplinary tasks in the fields of science, technology, engineering and mathematics - STEM.

Physical simulation requires interdisciplinary work: physical modeling, programming, mathematics, programming, geometry, graphic programming. The collection of exercises introduces this world step by step.

Exercise Sheet 1: Mass-Spring-Pendulum

Create physical model for mass-spring-pendulum. Simulation.

  • mass, force, acceleration
  • Hooke's law

Exercise Sheet 2: Mass-Spring-Double-Pendulum

Simulation of a physical system consisting of two masses and two springs.

  • masses, forces, acceleration
  • linear springs

Exercise Sheet 3: House

Draw a house of lines and circles.

  • coordinates
  • elementary graphics commands
  • methods with parameters
  • for loops

Exercise Sheet 4: House Configurator

A configurable house. Parameters control the shape of the house.

  • methods with parameters
  • geometrical calculations with coordinates
  • intercept theorem

Exercise Sheet 5: Rolling Ball

Ball rolls on a horizontal base. Rolling ball crashes against the wall.

  • rolling friction
  • air resistance
  • collision
  • trigonometry
  • physical events
  • triggers (thresholds)

Exercise sheet 6: Projectile Motion

The throwing of a ball. The ball experiences a flow resistance force through the air.

  • air resistance force
  • triggers

Exercise Sheet 7: Locomotive

Draw an animated locomotive from lines and circles.

  • trigonometry
  • methods
  • for loops
  • animated, time-dependent graphics (videos)

Exercise Sheet 8: Satellite

A satellite on its orbit around the earth.

  • law of gravity
  • orbits of celestial bodies

Exercise Sheet 9: Satellites, Object Oriented Programming

Several satellites orbit earth. They are forced into orbit by the gravity of the earth.

  • physical modeling with vector calculation
  • object oriented programming of the celestial bodies: class, instance, object attribute, object method

Exercise Sheet 10: Belousov-Zhabotinsky Reaction

An aqueous solution with several chemical substances. Chemical reactions continuously change the concentration of substances. This results in oscillating behavior.

  • stoichiometric reaction equations
  • physical modeling

Exercise Sheet 11: Geometric Transformations

Geometric transformations used in graphics programming. Coordinate transformations affect drawing commands and change the coordinates used in drawing commands.

  • geometric transfomations
  • translation, rotation, scaling, point reflection, axis reflection

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