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myPhysicsLab Billiards. formation. one hits three one hits six. offset speed damping elasticity show forces show energy show clock pan-zoom time step time rate Diff Eq Solver. Eulers Method Modified Euler Runge-Kutta Adaptive Step-Modified Euler Adaptive Step-Runge-Kutta. potential energy offset background. MYPHYSICSLAB DO NOTHING GRINDER Physics-based simulation of a trammel of Archimedes, also known as a "do nothing machine" or "do nothing grinder".Uses the 2D Rigid Body Physics Engine.. Click near the handle with your mouse to apply a spring force. Turn on "extra block" to see the mechanism collide withanother block.
MYPHYSICSLAB MOVEABLE DOUBLE PENDULUMONLINE PENDULUMPENDULUM LABSIMPLE PENDULUM SIMULATIONYES OR NO PENDULUM ONLINE Physics-based simulation of a double pendulum whose support point is moveable. Click near the support point to drag it with your mouse. You can also reposition the pendulum masses. MYPHYSICSLAB MUTUAL ATTRACTION Physics-based simulation of objects under an inverse square gravity law using the 2D Rigid Body Physics Engine.. Change parameters such as gravity, damping, elasticity of MYPHYSICSLAB MOLECULE 3MOLECULE 3 PERFUMEMOLECULE 3 AIRTEC MATTRESS TOPPERNH 3 MOLECULEOMEGA 3 MOLECULEPO4 3 MOLECULECHAPTER 3 MOLECULESOF LIFE
This simulation shows 3 masses connected by springs and free to move in 2 dimensions. You can change parameters in the simulation such as gravity, mass, spring stiffness, and MYPHYSICSLAB NEWTON'S CRADLE Simulation of Newton's Cradle, a device consisting of several steel balls suspended from a cage.Uses the 2D Rigid Body Physics Engine.. Each ball acts like an individual pendulum. At rest all the balls are touching. The surprising thing is that when you lift one of the end balls and let it hit the resting balls, only the ball at the other end moves, and the initial ball stops at rest. MYPHYSICSLAB BRACHISTOCHRONE The brachistochrone curve can be generated by tracking a point on the rim of a wheel as it rolls on the ground. The general equation for the brachistochrone is given parametrically as. x= a(θ −sinθ)+x0 x = a ( θ − sin. . θ) + x 0. y = −a(1−cosθ)+y0 y = − a ( 1 − cos. . θ) + y 0. MYPHYSICSLAB HOME PAGEPENDULUMNUMERICAL ANALYSISNEWTON'S CRADLEDOUBLE SPRINGCHAIN OF SPRINGSMUTUAL ATTRACTION Customize and Share. There are several ways to reproduce a particular experimental setup. The easiest way is to click the "share" button. Modify the simulation by changing parameters such as gravity, damping, and by dragging objects with your mouse. MYPHYSICSLAB SIMPLE PENDULUMSEE MORE ON MYPHYSICSLAB.COM MYPHYSICSLAB DOUBLE PENDULUM This is a simulation of a double pendulum. For large motions it is a chaotic system, but for small motions it is a simple linear system. You can change parameters in the MYPHYSICSLAB BILLIARDSBILLIARDS FREE PLAY ONLINEBILLIARDS 8 BALL WITHCOMPUTER
myPhysicsLab Billiards. formation. one hits three one hits six. offset speed damping elasticity show forces show energy show clock pan-zoom time step time rate Diff Eq Solver. Eulers Method Modified Euler Runge-Kutta Adaptive Step-Modified Euler Adaptive Step-Runge-Kutta. potential energy offset background. MYPHYSICSLAB DO NOTHING GRINDER Physics-based simulation of a trammel of Archimedes, also known as a "do nothing machine" or "do nothing grinder".Uses the 2D Rigid Body Physics Engine.. Click near the handle with your mouse to apply a spring force. Turn on "extra block" to see the mechanism collide withanother block.
MYPHYSICSLAB MOVEABLE DOUBLE PENDULUMONLINE PENDULUMPENDULUM LABSIMPLE PENDULUM SIMULATIONYES OR NO PENDULUM ONLINE Physics-based simulation of a double pendulum whose support point is moveable. Click near the support point to drag it with your mouse. You can also reposition the pendulum masses. MYPHYSICSLAB MUTUAL ATTRACTION Physics-based simulation of objects under an inverse square gravity law using the 2D Rigid Body Physics Engine.. Change parameters such as gravity, damping, elasticity of MYPHYSICSLAB MOLECULE 3MOLECULE 3 PERFUMEMOLECULE 3 AIRTEC MATTRESS TOPPERNH 3 MOLECULEOMEGA 3 MOLECULEPO4 3 MOLECULECHAPTER 3 MOLECULESOF LIFE
This simulation shows 3 masses connected by springs and free to move in 2 dimensions. You can change parameters in the simulation such as gravity, mass, spring stiffness, and MYPHYSICSLAB NEWTON'S CRADLE Simulation of Newton's Cradle, a device consisting of several steel balls suspended from a cage.Uses the 2D Rigid Body Physics Engine.. Each ball acts like an individual pendulum. At rest all the balls are touching. The surprising thing is that when you lift one of the end balls and let it hit the resting balls, only the ball at the other end moves, and the initial ball stops at rest. MYPHYSICSLAB BRACHISTOCHRONE The brachistochrone curve can be generated by tracking a point on the rim of a wheel as it rolls on the ground. The general equation for the brachistochrone is given parametrically as. x= a(θ −sinθ)+x0 x = a ( θ − sin. . θ) + x 0. y = −a(1−cosθ)+y0 y = − a ( 1 − cos. . θ) + y 0. MYPHYSICSLAB ROLLER COASTER Physics of the Simple Roller Coaster. roller coaster variables. A ball moves along a curved track. We assume that the ball cannot leave the track, but is free to move along its length. We have two variables. p = position on the track (measured by path length along the track) v = velocity. We pick some point on the track to be position p = 0 and MYPHYSICSLAB MOLECULE 3 This simulation shows 3 masses connected by springs and free to move in 2 dimensions. You can change parameters in the simulation such as gravity, mass, spring stiffness, and MYPHYSICSLAB PENDULUM CLOCK myPhysicsLab Pendulum Clock. with gears extra body pendulum length turning force gravity damping elasticity show forces show energy show clock pan-zoom time step time rate Diff Eq Solver. Eulers Method Modified Euler Runge-Kutta Adaptive Step-Modified Euler Adaptive Step-Runge-Kutta. potential energy offset background. MYPHYSICSLAB RIGID BODY FORCES This simulation uses the Rigid Body Physics Engine to show objects moving in 2 dimensions with various forces applied. Click near an object to exert a spring force with your mouse. With the keyboard you can control four "thrusters". The keys S,D,F,E control thrust on block1. The keys J,K,L,I (and also the arrow keys) control thrust onblock2.
MYPHYSICSLAB SINGLE SPRING show sim. terminal. command >. This simulation shows a single mass on a spring, which is connected to a wall. This is an example of a simple linear oscillator. You can change mass, spring stiffness, and friction (damping). You can drag the mass with your mouse to change the starting position. The math behind the simulation is shown below. MYPHYSICSLAB DOUBLE 2D SPRING Here are the equations of motion. The derivation is similar to that given for the Single 2D Spring. F 1x = m 1 a 1x = −k 1 S 1 sin θ 1 − b 1 v 1x + k 2 S 2 sin θ 2 F 1y = m 1 a 1y = −k 1 S 1 cos θ 1 − b 1 v 1y + k 2 S 2 cos θ 2 + m 1 g F 2x = m 2 a 2x = −k 2 S 2 sin θ 2 − b 2 v 2x F 2y = m 2 a 2y = −k 2 S 2 cos θ 2 − b 2 v 2y + m 2 g . The spring stretch S n and angles θ MYPHYSICSLAB MOVEABLE PENDULUM Moveable Pendulum. Physics-based simulation of a pendulum attached to a moveable support point or "anchor block". The support point is assumed to be so massive that it is not affected by the pendulum. You can drag the anchor block or pendulum with your mouse. Change parameters like gravity, pendulum length, damping, etc. MYPHYSICSLAB RIGID BODY ROLLER COASTER Rigid Body Roller Coaster. path. Hump Loop Circle Oval Lemniscate Cardioid Spiral Flat. gravity damping elasticity show forces show energy show clock pan-zoom time step time rate Diff Eq Solver. Eulers Method Modified Euler Runge-Kutta Adaptive Step-Modified Euler Adaptive Step-Runge-Kutta. potential energy offset background. MYPHYSICSLAB CLASSIFYING DIFFERENTIAL EQUATIONS Homogeneous vs. Non-homogeneous. This is another way of classifying differential equations. These fancy terms amount to the following: whether there is a term involving only time, t (shown on the right hand side in equations below). x '' + 2_x' + x = 0 is homogeneous. x '' + 2_x' + x = sin ( t) is non-homogeneous. x ' + t2x = 0 ishomogeneous.
MYPHYSICSLAB COLLIDE SPRINGS This simulation explores using small stiff springs to do collision handling. You can change the number of blocks (from 1 to 3) and theirstarting positions.
MYPHYSICSLAB HOME PAGEPENDULUMNUMERICAL ANALYSISNEWTON'S CRADLEDOUBLE SPRINGCHAIN OF SPRINGSMUTUAL ATTRACTION Customize and Share. There are several ways to reproduce a particular experimental setup. The easiest way is to click the "share" button. Modify the simulation by changing parameters such as gravity, damping, and by dragging objects with your mouse. MYPHYSICSLAB SIMPLE PENDULUMSEE MORE ON MYPHYSICSLAB.COM MYPHYSICSLAB DOUBLE PENDULUM This is a simulation of a double pendulum. For large motions it is a chaotic system, but for small motions it is a simple linear system. You can change parameters in the MYPHYSICSLAB BILLIARDSBILLIARDS FREE PLAY ONLINEBILLIARDS 8 BALL WITHCOMPUTER
myPhysicsLab Billiards. formation. one hits three one hits six. offset speed damping elasticity show forces show energy show clock pan-zoom time step time rate Diff Eq Solver. Eulers Method Modified Euler Runge-Kutta Adaptive Step-Modified Euler Adaptive Step-Runge-Kutta. potential energy offset background. MYPHYSICSLAB DO NOTHING GRINDER Physics-based simulation of a trammel of Archimedes, also known as a "do nothing machine" or "do nothing grinder".Uses the 2D Rigid Body Physics Engine.. Click near the handle with your mouse to apply a spring force. Turn on "extra block" to see the mechanism collide withanother block.
MYPHYSICSLAB MOVEABLE DOUBLE PENDULUMONLINE PENDULUMPENDULUM LABSIMPLE PENDULUM SIMULATIONYES OR NO PENDULUM ONLINE Physics-based simulation of a double pendulum whose support point is moveable. Click near the support point to drag it with your mouse. You can also reposition the pendulum masses. MYPHYSICSLAB MUTUAL ATTRACTION Physics-based simulation of objects under an inverse square gravity law using the 2D Rigid Body Physics Engine.. Change parameters such as gravity, damping, elasticity of MYPHYSICSLAB MOLECULE 3MOLECULE 3 PERFUMEMOLECULE 3 AIRTEC MATTRESS TOPPERNH 3 MOLECULEOMEGA 3 MOLECULEPO4 3 MOLECULECHAPTER 3 MOLECULESOF LIFE
This simulation shows 3 masses connected by springs and free to move in 2 dimensions. You can change parameters in the simulation such as gravity, mass, spring stiffness, and MYPHYSICSLAB NEWTON'S CRADLE Simulation of Newton's Cradle, a device consisting of several steel balls suspended from a cage.Uses the 2D Rigid Body Physics Engine.. Each ball acts like an individual pendulum. At rest all the balls are touching. The surprising thing is that when you lift one of the end balls and let it hit the resting balls, only the ball at the other end moves, and the initial ball stops at rest. MYPHYSICSLAB BRACHISTOCHRONE The brachistochrone curve can be generated by tracking a point on the rim of a wheel as it rolls on the ground. The general equation for the brachistochrone is given parametrically as. x= a(θ −sinθ)+x0 x = a ( θ − sin. . θ) + x 0. y = −a(1−cosθ)+y0 y = − a ( 1 − cos. . θ) + y 0. MYPHYSICSLAB HOME PAGEPENDULUMNUMERICAL ANALYSISNEWTON'S CRADLEDOUBLE SPRINGCHAIN OF SPRINGSMUTUAL ATTRACTION Customize and Share. There are several ways to reproduce a particular experimental setup. The easiest way is to click the "share" button. Modify the simulation by changing parameters such as gravity, damping, and by dragging objects with your mouse. MYPHYSICSLAB SIMPLE PENDULUMSEE MORE ON MYPHYSICSLAB.COM MYPHYSICSLAB DOUBLE PENDULUM This is a simulation of a double pendulum. For large motions it is a chaotic system, but for small motions it is a simple linear system. You can change parameters in the MYPHYSICSLAB BILLIARDSBILLIARDS FREE PLAY ONLINEBILLIARDS 8 BALL WITHCOMPUTER
myPhysicsLab Billiards. formation. one hits three one hits six. offset speed damping elasticity show forces show energy show clock pan-zoom time step time rate Diff Eq Solver. Eulers Method Modified Euler Runge-Kutta Adaptive Step-Modified Euler Adaptive Step-Runge-Kutta. potential energy offset background. MYPHYSICSLAB DO NOTHING GRINDER Physics-based simulation of a trammel of Archimedes, also known as a "do nothing machine" or "do nothing grinder".Uses the 2D Rigid Body Physics Engine.. Click near the handle with your mouse to apply a spring force. Turn on "extra block" to see the mechanism collide withanother block.
MYPHYSICSLAB MOVEABLE DOUBLE PENDULUMONLINE PENDULUMPENDULUM LABSIMPLE PENDULUM SIMULATIONYES OR NO PENDULUM ONLINE Physics-based simulation of a double pendulum whose support point is moveable. Click near the support point to drag it with your mouse. You can also reposition the pendulum masses. MYPHYSICSLAB MUTUAL ATTRACTION Physics-based simulation of objects under an inverse square gravity law using the 2D Rigid Body Physics Engine.. Change parameters such as gravity, damping, elasticity of MYPHYSICSLAB MOLECULE 3MOLECULE 3 PERFUMEMOLECULE 3 AIRTEC MATTRESS TOPPERNH 3 MOLECULEOMEGA 3 MOLECULEPO4 3 MOLECULECHAPTER 3 MOLECULESOF LIFE
This simulation shows 3 masses connected by springs and free to move in 2 dimensions. You can change parameters in the simulation such as gravity, mass, spring stiffness, and MYPHYSICSLAB NEWTON'S CRADLE Simulation of Newton's Cradle, a device consisting of several steel balls suspended from a cage.Uses the 2D Rigid Body Physics Engine.. Each ball acts like an individual pendulum. At rest all the balls are touching. The surprising thing is that when you lift one of the end balls and let it hit the resting balls, only the ball at the other end moves, and the initial ball stops at rest. MYPHYSICSLAB BRACHISTOCHRONE The brachistochrone curve can be generated by tracking a point on the rim of a wheel as it rolls on the ground. The general equation for the brachistochrone is given parametrically as. x= a(θ −sinθ)+x0 x = a ( θ − sin. . θ) + x 0. y = −a(1−cosθ)+y0 y = − a ( 1 − cos. . θ) + y 0. MYPHYSICSLAB ROLLER COASTER Physics of the Simple Roller Coaster. roller coaster variables. A ball moves along a curved track. We assume that the ball cannot leave the track, but is free to move along its length. We have two variables. p = position on the track (measured by path length along the track) v = velocity. We pick some point on the track to be position p = 0 and MYPHYSICSLAB MOLECULE 3 This simulation shows 3 masses connected by springs and free to move in 2 dimensions. You can change parameters in the simulation such as gravity, mass, spring stiffness, and MYPHYSICSLAB PENDULUM CLOCK myPhysicsLab Pendulum Clock. with gears extra body pendulum length turning force gravity damping elasticity show forces show energy show clock pan-zoom time step time rate Diff Eq Solver. Eulers Method Modified Euler Runge-Kutta Adaptive Step-Modified Euler Adaptive Step-Runge-Kutta. potential energy offset background. MYPHYSICSLAB RIGID BODY FORCES This simulation uses the Rigid Body Physics Engine to show objects moving in 2 dimensions with various forces applied. Click near an object to exert a spring force with your mouse. With the keyboard you can control four "thrusters". The keys S,D,F,E control thrust on block1. The keys J,K,L,I (and also the arrow keys) control thrust onblock2.
MYPHYSICSLAB SINGLE SPRING show sim. terminal. command >. This simulation shows a single mass on a spring, which is connected to a wall. This is an example of a simple linear oscillator. You can change mass, spring stiffness, and friction (damping). You can drag the mass with your mouse to change the starting position. The math behind the simulation is shown below. MYPHYSICSLAB DOUBLE 2D SPRING Here are the equations of motion. The derivation is similar to that given for the Single 2D Spring. F 1x = m 1 a 1x = −k 1 S 1 sin θ 1 − b 1 v 1x + k 2 S 2 sin θ 2 F 1y = m 1 a 1y = −k 1 S 1 cos θ 1 − b 1 v 1y + k 2 S 2 cos θ 2 + m 1 g F 2x = m 2 a 2x = −k 2 S 2 sin θ 2 − b 2 v 2x F 2y = m 2 a 2y = −k 2 S 2 cos θ 2 − b 2 v 2y + m 2 g . The spring stretch S n and angles θ MYPHYSICSLAB RIGID BODY ROLLER COASTER Rigid Body Roller Coaster. path. Hump Loop Circle Oval Lemniscate Cardioid Spiral Flat. gravity damping elasticity show forces show energy show clock pan-zoom time step time rate Diff Eq Solver. Eulers Method Modified Euler Runge-Kutta Adaptive Step-Modified Euler Adaptive Step-Runge-Kutta. potential energy offset background. MYPHYSICSLAB MOVEABLE PENDULUM Moveable Pendulum. Physics-based simulation of a pendulum attached to a moveable support point or "anchor block". The support point is assumed to be so massive that it is not affected by the pendulum. You can drag the anchor block or pendulum with your mouse. Change parameters like gravity, pendulum length, damping, etc. MYPHYSICSLAB CLASSIFYING DIFFERENTIAL EQUATIONS Homogeneous vs. Non-homogeneous. This is another way of classifying differential equations. These fancy terms amount to the following: whether there is a term involving only time, t (shown on the right hand side in equations below). x '' + 2_x' + x = 0 is homogeneous. x '' + 2_x' + x = sin ( t) is non-homogeneous. x ' + t2x = 0 ishomogeneous.
MYPHYSICSLAB COLLIDE SPRINGS This simulation explores using small stiff springs to do collision handling. You can change the number of blocks (from 1 to 3) and theirstarting positions.
MYPHYSICSLAB HOME PAGEPENDULUMNUMERICAL ANALYSISNEWTON'S CRADLEDOUBLE SPRINGCHAIN OF SPRINGSMUTUAL ATTRACTION Customize and Share. There are several ways to reproduce a particular experimental setup. The easiest way is to click the "share" button. Modify the simulation by changing parameters such as gravity, damping, and by dragging objects with your mouse. MYPHYSICSLAB SIMPLE PENDULUMSEE MORE ON MYPHYSICSLAB.COM MYPHYSICSLAB DOUBLE PENDULUM This is a simulation of a double pendulum. For large motions it is a chaotic system, but for small motions it is a simple linear system. You can change parameters in the MYPHYSICSLAB BILLIARDSBILLIARDS FREE PLAY ONLINEBILLIARDS 8 BALL WITHCOMPUTER
myPhysicsLab Billiards. formation. one hits three one hits six. offset speed damping elasticity show forces show energy show clock pan-zoom time step time rate Diff Eq Solver. Eulers Method Modified Euler Runge-Kutta Adaptive Step-Modified Euler Adaptive Step-Runge-Kutta. potential energy offset background. MYPHYSICSLAB DO NOTHING GRINDER Physics-based simulation of a trammel of Archimedes, also known as a "do nothing machine" or "do nothing grinder".Uses the 2D Rigid Body Physics Engine.. Click near the handle with your mouse to apply a spring force. Turn on "extra block" to see the mechanism collide withanother block.
MYPHYSICSLAB MOVEABLE DOUBLE PENDULUMONLINE PENDULUMPENDULUM LABSIMPLE PENDULUM SIMULATIONYES OR NO PENDULUM ONLINE Physics-based simulation of a double pendulum whose support point is moveable. Click near the support point to drag it with your mouse. You can also reposition the pendulum masses. MYPHYSICSLAB MUTUAL ATTRACTION Physics-based simulation of objects under an inverse square gravity law using the 2D Rigid Body Physics Engine.. Change parameters such as gravity, damping, elasticity of MYPHYSICSLAB MOLECULE 3MOLECULE 3 PERFUMEMOLECULE 3 AIRTEC MATTRESS TOPPERNH 3 MOLECULEOMEGA 3 MOLECULEPO4 3 MOLECULECHAPTER 3 MOLECULESOF LIFE
This simulation shows 3 masses connected by springs and free to move in 2 dimensions. You can change parameters in the simulation such as gravity, mass, spring stiffness, and MYPHYSICSLAB NEWTON'S CRADLE Simulation of Newton's Cradle, a device consisting of several steel balls suspended from a cage.Uses the 2D Rigid Body Physics Engine.. Each ball acts like an individual pendulum. At rest all the balls are touching. The surprising thing is that when you lift one of the end balls and let it hit the resting balls, only the ball at the other end moves, and the initial ball stops at rest. MYPHYSICSLAB BRACHISTOCHRONE The brachistochrone curve can be generated by tracking a point on the rim of a wheel as it rolls on the ground. The general equation for the brachistochrone is given parametrically as. x= a(θ −sinθ)+x0 x = a ( θ − sin. . θ) + x 0. y = −a(1−cosθ)+y0 y = − a ( 1 − cos. . θ) + y 0. MYPHYSICSLAB HOME PAGEPENDULUMNUMERICAL ANALYSISNEWTON'S CRADLEDOUBLE SPRINGCHAIN OF SPRINGSMUTUAL ATTRACTION Customize and Share. There are several ways to reproduce a particular experimental setup. The easiest way is to click the "share" button. Modify the simulation by changing parameters such as gravity, damping, and by dragging objects with your mouse. MYPHYSICSLAB SIMPLE PENDULUMSEE MORE ON MYPHYSICSLAB.COM MYPHYSICSLAB DOUBLE PENDULUM This is a simulation of a double pendulum. For large motions it is a chaotic system, but for small motions it is a simple linear system. You can change parameters in the MYPHYSICSLAB BILLIARDSBILLIARDS FREE PLAY ONLINEBILLIARDS 8 BALL WITHCOMPUTER
myPhysicsLab Billiards. formation. one hits three one hits six. offset speed damping elasticity show forces show energy show clock pan-zoom time step time rate Diff Eq Solver. Eulers Method Modified Euler Runge-Kutta Adaptive Step-Modified Euler Adaptive Step-Runge-Kutta. potential energy offset background. MYPHYSICSLAB DO NOTHING GRINDER Physics-based simulation of a trammel of Archimedes, also known as a "do nothing machine" or "do nothing grinder".Uses the 2D Rigid Body Physics Engine.. Click near the handle with your mouse to apply a spring force. Turn on "extra block" to see the mechanism collide withanother block.
MYPHYSICSLAB MOVEABLE DOUBLE PENDULUMONLINE PENDULUMPENDULUM LABSIMPLE PENDULUM SIMULATIONYES OR NO PENDULUM ONLINE Physics-based simulation of a double pendulum whose support point is moveable. Click near the support point to drag it with your mouse. You can also reposition the pendulum masses. MYPHYSICSLAB MUTUAL ATTRACTION Physics-based simulation of objects under an inverse square gravity law using the 2D Rigid Body Physics Engine.. Change parameters such as gravity, damping, elasticity of MYPHYSICSLAB MOLECULE 3MOLECULE 3 PERFUMEMOLECULE 3 AIRTEC MATTRESS TOPPERNH 3 MOLECULEOMEGA 3 MOLECULEPO4 3 MOLECULECHAPTER 3 MOLECULESOF LIFE
This simulation shows 3 masses connected by springs and free to move in 2 dimensions. You can change parameters in the simulation such as gravity, mass, spring stiffness, and MYPHYSICSLAB NEWTON'S CRADLE Simulation of Newton's Cradle, a device consisting of several steel balls suspended from a cage.Uses the 2D Rigid Body Physics Engine.. Each ball acts like an individual pendulum. At rest all the balls are touching. The surprising thing is that when you lift one of the end balls and let it hit the resting balls, only the ball at the other end moves, and the initial ball stops at rest. MYPHYSICSLAB BRACHISTOCHRONE The brachistochrone curve can be generated by tracking a point on the rim of a wheel as it rolls on the ground. The general equation for the brachistochrone is given parametrically as. x= a(θ −sinθ)+x0 x = a ( θ − sin. . θ) + x 0. y = −a(1−cosθ)+y0 y = − a ( 1 − cos. . θ) + y 0. MYPHYSICSLAB ROLLER COASTER Physics of the Simple Roller Coaster. roller coaster variables. A ball moves along a curved track. We assume that the ball cannot leave the track, but is free to move along its length. We have two variables. p = position on the track (measured by path length along the track) v = velocity. We pick some point on the track to be position p = 0 and MYPHYSICSLAB MOLECULE 3 This simulation shows 3 masses connected by springs and free to move in 2 dimensions. You can change parameters in the simulation such as gravity, mass, spring stiffness, and MYPHYSICSLAB PENDULUM CLOCK myPhysicsLab Pendulum Clock. with gears extra body pendulum length turning force gravity damping elasticity show forces show energy show clock pan-zoom time step time rate Diff Eq Solver. Eulers Method Modified Euler Runge-Kutta Adaptive Step-Modified Euler Adaptive Step-Runge-Kutta. potential energy offset background. MYPHYSICSLAB RIGID BODY FORCES This simulation uses the Rigid Body Physics Engine to show objects moving in 2 dimensions with various forces applied. Click near an object to exert a spring force with your mouse. With the keyboard you can control four "thrusters". The keys S,D,F,E control thrust on block1. The keys J,K,L,I (and also the arrow keys) control thrust onblock2.
MYPHYSICSLAB SINGLE SPRING show sim. terminal. command >. This simulation shows a single mass on a spring, which is connected to a wall. This is an example of a simple linear oscillator. You can change mass, spring stiffness, and friction (damping). You can drag the mass with your mouse to change the starting position. The math behind the simulation is shown below. MYPHYSICSLAB DOUBLE 2D SPRING Here are the equations of motion. The derivation is similar to that given for the Single 2D Spring. F 1x = m 1 a 1x = −k 1 S 1 sin θ 1 − b 1 v 1x + k 2 S 2 sin θ 2 F 1y = m 1 a 1y = −k 1 S 1 cos θ 1 − b 1 v 1y + k 2 S 2 cos θ 2 + m 1 g F 2x = m 2 a 2x = −k 2 S 2 sin θ 2 − b 2 v 2x F 2y = m 2 a 2y = −k 2 S 2 cos θ 2 − b 2 v 2y + m 2 g . The spring stretch S n and angles θ MYPHYSICSLAB RIGID BODY ROLLER COASTER Rigid Body Roller Coaster. path. Hump Loop Circle Oval Lemniscate Cardioid Spiral Flat. gravity damping elasticity show forces show energy show clock pan-zoom time step time rate Diff Eq Solver. Eulers Method Modified Euler Runge-Kutta Adaptive Step-Modified Euler Adaptive Step-Runge-Kutta. potential energy offset background. MYPHYSICSLAB MOVEABLE PENDULUM Moveable Pendulum. Physics-based simulation of a pendulum attached to a moveable support point or "anchor block". The support point is assumed to be so massive that it is not affected by the pendulum. You can drag the anchor block or pendulum with your mouse. Change parameters like gravity, pendulum length, damping, etc. MYPHYSICSLAB CLASSIFYING DIFFERENTIAL EQUATIONS Homogeneous vs. Non-homogeneous. This is another way of classifying differential equations. These fancy terms amount to the following: whether there is a term involving only time, t (shown on the right hand side in equations below). x '' + 2_x' + x = 0 is homogeneous. x '' + 2_x' + x = sin ( t) is non-homogeneous. x ' + t2x = 0 ishomogeneous.
MYPHYSICSLAB COLLIDE SPRINGS This simulation explores using small stiff springs to do collision handling. You can change the number of blocks (from 1 to 3) and theirstarting positions.
PHYSICS SIMULATIONS
English German previous next Click on one of the physics simulations below... you'll see them animating in real time, and be able to interact with them by dragging objects or changing parameters like gravity.Single Spring
Double Spring
Pendulum
Pendulum with
Direction Field
Chaotic Pendulum
Two Chaotic
Pendulums
Moveable
Pendulum
Double Pendulum
Moveable
Double Pendulum
Inverted
Vibrating Pendulum
Inverted
Double Pendulum
2D Spring
Double
2D Spring
Colliding Blocks
Cart + Pendulum
Dangling Stick
Rigid Body
Forces
Rigid Body
Collisions
Rigid Body
Contact Forces
Roller Coaster
Roller Coaster
with Spring
Roller Coaster
with Two Balls
Roller Coaster
with Flight
Rigid Body
Roller Coaster
Brachistochrone
Billiards
Hanging Chain
Newton's Cradle
Do Nothing
Grinder
Pendulum Clock
Car Suspension
Double Pendulum
with Physics Engine
Cart + Pendulum
with Physics Engine
Mars Moon
Curved Objects
Pile
Pile Attract
Polygon Shapes
String
Rigid Double PendulumCompare
Double Pendulums
Molecule 2
Molecule 3
Molecule 4
Molecule 5
Molecule 6
Chain Of Springs
Collide Springs
Reaction Force
Pendulum
Mutual Attraction
CUSTOMIZE AND SHARE
There are several ways to reproduce a particular experimental setup. The easiest way is to click the "share" button. * Modify the simulation by changing parameters such as gravity, damping, and by dragging objects with your mouse. * Click the "share" button. Copy the URL from the dialog. * Paste the URL in an email. Or save it in a text file for lateruse.
When the recipient clicks the URL, the EasyScript that is embedded in the URL will replicate the conditions that you set up. See Customizing myPhysicsLab Simulations for how to customize further with JavaScript or EasyScript. OPEN SOURCE SOFTWARE myPhysicsLab is provided as open source software under the Apache 2.0 License . Source code is available at https://github.com/myphysicslab/myphysicslab. Online documentationis available.
There are around 50 different simulations in the source code, each of which has an _example file_ which is mainly for development and testing. These can also be used to _show simulations offline_ (when not connected to the internet). The example files are available online in two forms: * advanced-compiled which loads faster. Downloadable version for offlineusage.
* simple-compiled which allows for more customization. Downloadable version foroffline usage.
HOW DOES IT WORK?
Most of the simulation web pages show how the math is derived. See for example the Single Springsimulation.
* A physics simulation starts with a _mathematical model_ whose variables define the state of the system at a given time. Each variable represents the position or velocity of some part of thesystem.
* The heart of a physics simulation is the set of differential equations that describe how the variables evolve over time. The forces and geometry determine theequations.
* The next step is _getting the computer to solve the equations_, a process that goes by the name numerical analysis . The Runge Kutta method is a popular choice. * For simulations that involve _collisions_ there are additional steps: we need to detect the collision and then back up in time to the moment before the collision to modify the velocities. * Finally, there are lots of programming details about how to represent objects on the computer display, how to handle user input , how to synchronize withreal time ,
and so on.
The rigid body physics engine is the most sophisticated simulation shown here. It is capable of replicating all of the other more specialized simulations. The physics engine handles collisions and also calculates contact forces which allow objects to push against each other. See also links to other physics websites . UNITS OF MEASUREMENT The myPhysicsLab simulations do not have units of measurements specified such as meters, kilograms, seconds. The units are _dimensionless_, they can be interpreted however you want, but they must be _consistent within the simulation_. For example if we regard a unit of distance as _one meter_ and a unit of time as _one second_, then a unit of velocity must be _onemeter/second_.
See the discussion About Units Of Measurementin the
myPhysicsLab Documentation.E-MAIL LIST
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View previous campaigns.ABOUT THE AUTHOR
Hi, my name is Erik Neumann, I live in Seattle, WA, USA, and I am a self-employed software engineer. I started developing this website in 2001, both as a personal project to learn scientific computing, and with a vision of developing an online science museum. I grew up in Chicago near the Museum of Science and Industry which I loved to visit and learn aboutscience and math.
I got a BA in Mathematics at Oberlin College, Ohio, 1978, and an MBA from Univerity of Chicago, 1984. My first software jobs were using thelanguage APL
which I enjoyed for its math-like conciseness and power. I was fortunate to get involved in the Macintosh software industry early on in 1985, joining MacroMind , which became Macromedia . I led the software development at MacroMind as VP of Engineering for 5 years. Our most significant product was VideoWorks, which was renamed Director, and lives on today as Adobe Director . In the 1980's, the interactive multimedia concepts that are so common today were new and being developed. VideoWorks was mainly an animation tool, but also incorporated programmable interactivity. Our main competitors at that time were HyperCard, SuperCard, and Authorware. Director was used in many different ways; I am most proud that it became the preferred way to prototype software user interfaces for a time during the 90's. Director was also used to develop the introductory "guided tour" tutorial that came with the Macintosh in the early years. And of course, Director was used for all sorts of art, design, and marketingprojects.
I went on to work at Apple Computer on new multimedia and user interface concepts involving digital agents, animated user interfaces, speech recognition and distributed information access. In 1991, there was a sudden flurry of activity when Apple and IBM were trying to set up a strategic partnership. I became involved in the super-secret negotiations, and made the suggestion that what the world needed was a standard for multimedia that multimedia content creators could rely on to publish to (ultimately this is what HTML became). Based on these suggestions, Kaleida Labs was founded. Our work there developed a product called ScriptX, which
turned out to be very similar to Sun's Java which was being developed at the same time. ScriptX had goals of supporting all forms of multimedia: text, images, audio, video, animation; being cross-platform (Mac and Windows), interpreted, object oriented, with a garbage collector to manage memory. I then moved to Seattle and turned my attention back to mathematics and science. I relearned calculus by doing all the problems in my old college text book and took further math classes at the University of Washington. I started developing this website as a way to practice what I was learning. I am now happy to use excellent tools such as HTML and JavaScript, and leave their development to others. I continue to work on physics simulations, with several new ones in development. Archive of older projects. This web page was first published April 2001. Erik Neumann, 2004-2016 revised Feb 6 2021 previousnext
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