The following animation illustrates the operation of a PID controller using the example of a water level control system. Control behavior, manipulated variable, and disturbance influence are visualized in real time. Links Animation Description The animation shows a water tank as the controlled system (plant) with an inflow (manipulated variable) and an outflow (disturbance variable).… Read More »
This animation illustrates the different types of projectile motion – from free fall to horizontal, vertical, and oblique throws. A projectile moves along its trajectory while the velocity vector is decomposed into its horizontal and vertical components in real time. The launch angle, initial velocity, and time can be adjusted interactively. Links Description of the… Read More »
This animation simulates the chaotic behavior of a double pendulum – one of the most famous examples of deterministic chaos systems. Two coupled pendulum arms with adjustable lengths and masses swing under the influence of gravity. By interactively dragging the masses, any starting position can be set, while an angle-time diagram records the temporal evolution… Read More »
The animation illustrates the principle of Fourier synthesis: Complex periodic waveforms can be generated by superposition of simple sine waves (harmonics). Interactively, the number of harmonics can be varied and different target waveforms can be selected. Links Description of the animation The animation visualizes the Fourier series, which allows periodic functions to be represented as… Read More »
The animation simulates the physical behavior of ice cubes in a glass of water. By clicking or using a button, ice cubes can be created that fall into the water, submerge, and float to the surface due to buoyancy—an illustrative example of Archimedes’ principle. Links Description of the Animation The animation shows a glass filled… Read More »
The animation simulates the gravitational force between celestial bodies. Planets with different masses and initial velocities attract each other, form orbits, and can merge upon collision – an interactive model for exploring Newtonian gravitation. Links Description of the animation The animation shows a space with freely placeable planets that attract each other according to Newton’s… Read More »
The animation simulates a billiard shot to demonstrate the law of conservation of momentum. A white cue ball can be aimed at colored object balls, with the collisions showing momentum transfer between the balls. Links Description of the Animation The animation shows a billiard table with a white cue ball and six colored object balls… Read More »
The animation illustrates the relationship between circular motion and a harmonic wave. A rotating pointer in the circle generates a sinusoidal wave curve through its projection—a fundamental principle for understanding oscillations and waves. Links Description of the Animation The animation shows how uniform circular motion and harmonic oscillation are mathematically related. A point moving at… Read More »
The animation represents the mathematical description of a harmonic wave. The amplitude, wave number, and angular frequency can be adjusted interactively, causing the wave properties to update in real time. Links Description of the animation The animation visualizes the wave equation, which describes a harmonic wave in space and time: \[ y(x,t) = A \sin(kx… Read More »
In the animation, the forces acting on the airfoil profile of an aircraft are displayed. An aircraft with a Clark Y airfoil is shown. The angle of attack of the wing can be varied. The forces represented as vectors adjust accordingly. Links Description of the Animation The lift force (blue) and the drag force (red)… Read More »