Mechanics Models

These models and simulations have been tagged “Mechanics”.

This shows the motion of a simple harmonic oscillator, described in terms of the natural frequency of oscillation. An accurate solution requires a small time step and RK4 as the integration algorithm.
This shows the motion of a simple harmonic oscillator, described in terms of the natural frequency of oscillation. An accurate solution requires a small time step and RK4 as the integration algorithm.
This shows the motion of a mass suspended from a spring, with damping. An accurate solution requires a small time step and RK4 as the integration algorithm.
This shows the motion of a mass suspended from a spring, with damping. An accurate solution requires a small time step and RK4 as the integration algorithm.
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.    Note that the equation has been made non-dimensional by measuring time in u
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.

Note that the equation has been made non-dimensional by measuring time in units of v_0/g, and distance in units of v_0^2/g. In these units, the acceleration due to gravity is simply 1. Also the "seconds" in the time axis of the graphs really means the time units defined here. Also in these units the initial speed is simply 1. 

The inclination has been fixed at Pi/2. A later version will let this change with a slider.

One of the displays is y vs. x, which shows the trajectory of the projectile. 
This shows the motion of a mass suspended from a spring. An accurate solution requires a small time step and RK4 as the integration algorithm.
This shows the motion of a mass suspended from a spring. An accurate solution requires a small time step and RK4 as the integration algorithm.
Model describing a simple pendulum with exact equation (but without dampening).
Model describing a simple pendulum with exact equation (but without dampening).
This shows the motion of a driven damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency.     The oscillator is driven with a force that is a sine function o
This shows the motion of a driven damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency. 

The oscillator is driven with a force that is a sine function of time, with a frequency that can be varied, expressed as a forcing ratio driving frequency/natural frequency.

An accurate solution requires a small time step and RK4 as the integration algorithm.
This shows the motion of a damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency. An accurate solution requires a small time step and RK4 as the integration
This shows the motion of a damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency. An accurate solution requires a small time step and RK4 as the integration algorithm.
This shows the motion of a driven damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency.     The oscillator is driven with a force that is a sine function o
This shows the motion of a driven damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency. 

The oscillator is driven with a force that is a sine function of time, with a frequency that can be varied, expressed as a forcing ratio driving frequency/natural frequency.

An accurate solution requires a small time step and RK4 as the integration algorithm.
A simple piston with rod length l and crank radius r.
A simple piston with rod length l and crank radius r.
This shows the motion of a mass suspended from a spring, with damping. An accurate solution requires a small time step and RK4 as the integration algorithm. (simplified clone)
This shows the motion of a mass suspended from a spring, with damping. An accurate solution requires a small time step and RK4 as the integration algorithm. (simplified clone)
This shows the motion of a driven damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency.     The oscillator is driven with a force that is a sine function o
This shows the motion of a driven damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency. 

The oscillator is driven with a force that is a sine function of time, with a frequency that can be varied, expressed as a forcing ratio driving frequency/natural frequency.

An accurate solution requires a small time step and RK4 as the integration algorithm.
This shows the motion of a damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency. An accurate solution requires a small time step and RK4 as the integration
This shows the motion of a damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency. An accurate solution requires a small time step and RK4 as the integration algorithm.
This shows the motion of a driven damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency.     The oscillator is driven with a force that is a sine function o
This shows the motion of a driven damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency. 

The oscillator is driven with a force that is a sine function of time, with a frequency that can be varied, expressed as a forcing ratio driving frequency/natural frequency.

An accurate solution requires a small time step and RK4 as the integration algorithm.
12 months ago
Ce modèle tente de simuler l'écroulement d'une pile d'étages les uns sur les autres, comme ce qui s'est passé le 11 septembre 2001 au World Trade Center. L'idée est que chaque dalle de béton tombe l'une après l'autre, en commençant par celle du haut, qui va se compacter avec celle d'en-dessous, puis
Ce modèle tente de simuler l'écroulement d'une pile d'étages les uns sur les autres, comme ce qui s'est passé le 11 septembre 2001 au World Trade Center.
L'idée est que chaque dalle de béton tombe l'une après l'autre, en commençant par celle du haut, qui va se compacter avec celle d'en-dessous, puis le bloc va tomber sur celle immédiatement inférieure, etc.
Lors de chacun des chocs, une certaine quantité d'énergie est dissipée sous forme de poussière, ce qui réduit d'autant la masse qui continue de descendre et la vitesse de celle-ci.
Le but est de voir comment se comporte la vitesse au fil du temps, ainsi que l'énergie totale accumulée.
L'énergie totale dégagée lors de l'effondrement se compte en Peta-Watt-heure, soit environ 11 jours de production d'une centrale nucléaire qui fonctionnerait à plein régime.
Model describing a simple pendulum with exact equation (but without dampening).
Model describing a simple pendulum with exact equation (but without dampening).
2 months ago
 Dieses Modell simuliert das Anfahren eines Gelenktriebwagens der Firma Stadler Rail. Mehr dazu im Video "Physik im Jahr 2053"  https://youtu.be/RMOv8A0MvyY
Dieses Modell simuliert das Anfahren eines Gelenktriebwagens der Firma Stadler Rail. Mehr dazu im Video "Physik im Jahr 2053"
https://youtu.be/RMOv8A0MvyY
This shows the motion of a mass suspended from a spring, with damping. An accurate solution requires a small time step and RK4 as the integration algorithm. (simplified clone)
This shows the motion of a mass suspended from a spring, with damping. An accurate solution requires a small time step and RK4 as the integration algorithm. (simplified clone)
12 hours ago