# Rope

### 1 collaborator

Uri Wilensky (Author)

### Tags

chemistry and physics

Tagged by Reuven M. Lerner almost 6 years ago

waves

Tagged by Reuven M. Lerner almost 6 years ago

Model group CCL | Visible to everyone | Changeable by group members (CCL)
Model was written in NetLogo 5.0.4 • Viewed 157 times • Downloaded 14 times • Run 0 times

## WHAT IS IT?

This project simulates a wave moving along a rope. The right end of the rope (shown in blue) is fixed to a wall. The left end of the rope (shown in green) provides an input, moving up and down in a sinusoidal motion. This creates a wave that travels along the rope.

## HOW IT WORKS

The rope is made up of a line of turtles. The turtle are fixed horizontally, but can move up and down. Each turtle acts as it were connected to its two neighboring turtles with springs. When a neighboring turtle is farther away, it exerts a stronger force.

When the left end of the rope (the green turtle) moves up, it "pulls up" the turtle to its right, which in turn pulls up the turtle to its right, and so on. In that way, a wave moves down the rope. When the wave reaches the right end of the rope (the blue turtle), the wave is reflected back to the left.

## HOW TO USE IT

Click the SETUP button to set up the rope. Click GO to make the left end of the rope (the green turtle) begin moving up and down.

The FRICTION slider controls the amount of friction in the rope. The FREQUENCY slider controls the speed with with the left end of the rope moves up and down. The AMPLITUDE slider controls the maximum height of the left end of the rope.

## THINGS TO NOTICE

There's a connection between the frequency with which the left end of the rope goes up and down and the number of peaks that emerge.

## THINGS TO TRY

Change the values on the sliders and observe what happens to the waves on the rope.

Try to create a "standing wave", in which some points on the rope do not move at all.

Change the blue turtle to green, so that there are two driving forces. Then change one of the red turtles in the middle of the rope to blue, so that there is a fixed point in the middle. What happens to the waves?

## EXTENDING THE MODEL

Change the right end of the rope so that it moves freely, rather than being fixed. How does that change the behavior of waves in the rope?

## NETLOGO FEATURES

For this project, it does not make sense for the turtles to "wrap" when they get to the top or bottom of the world. So the real y-position of the turtles is kept in a new variable (`ypos`), and the turtle is hidden if `ycor`, its true position, is beyond the boundaries of the world.

## HOW TO CITE

If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:

• Wilensky, U. (1997). NetLogo Rope model. http://ccl.northwestern.edu/netlogo/models/Rope. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.
• Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.

This model was created as part of the project: CONNECTED MATHEMATICS: MAKING SENSE OF COMPLEX PHENOMENA THROUGH BUILDING OBJECT-BASED PARALLEL MODELS (OBPML). The project gratefully acknowledges the support of the National Science Foundation (Applications of Advanced Technologies Program) -- grant numbers RED #9552950 and REC #9632612.

This model was developed at the MIT Media Lab using CM StarLogo. See Resnick, M. (1994) "Turtles, Termites and Traffic Jams: Explorations in Massively Parallel Microworlds." Cambridge, MA: MIT Press. Adapted to StarLogoT, 1997, as part of the Connected Mathematics Project.

This model was converted to NetLogo as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227. Converted from StarLogoT to NetLogo, 2001.

Click to Run Model

```turtles-own [
yvel           ;; velocity along the y axis
ypos           ;; y position (separate from ycor since we might exceed the boundaries of
;;   the world, which ycor can never do)
]

to setup
clear-all
set-default-shape turtles "circle"
create-turtles world-width [
set xcor who
set color red
set size 1.5                    ;; easier to see
if pxcor = max-pxcor
[ set color blue ]            ;; rightmost turtle is blue
if pxcor = min-pxcor
[ set color green ]           ;; leftmost turtle is green
]
reset-ticks
end

to go
ask turtles with [color = green]  ;; the green turtle is the driving force
[
ifelse ticks > 100  ;; ramp the force up gradually to avoid spikes in the wave
[ set ypos amplitude * sin (frequency * ticks) ]
[ set ypos (ticks / 100) * amplitude * sin (frequency * ticks) ]
ifelse patch-at 0 (ypos - ycor) != nobody ;; hide turtles outside the visible world
[
set ycor ypos
st
]
[ ht ]
]
ask turtles with [color = red]  ;;the red turtles respond to their neighbors' positions
[ ;; make your new y velocity equal to your old one + the average pos of your two neighbors
set yvel yvel + ((([ypos] of (turtle (who - 1))) - ypos) +
(([ypos] of (turtle (who + 1))) - ypos))
set yvel ((1000 - friction) / 1000) * yvel  ;; apply friction
]
;; we need two separate ask blocks here so all the turtles calculate their
;; new velocities before any turtles move
ask turtles with [color = red]
[ ;; calculate new y position
set ypos ypos + yvel                    ;; calculate new y position
ifelse patch-at 0 (ypos - ycor) != nobody ;; hide turtles outside the visible world
[ set ycor ypos
show-turtle ]
[ hide-turtle ]
]
tick
end

```

There are 10 versions of this model.

Uri Wilensky over 6 years ago Updated version tag Download this version
Uri Wilensky over 6 years ago Updated to version from NetLogo 5.0.3 distribution Download this version
Uri Wilensky over 7 years ago Updated to NetLogo 5.0 Download this version
Uri Wilensky almost 9 years ago Updated from NetLogo 4.1 Download this version
Uri Wilensky almost 9 years ago Updated from NetLogo 4.1 Download this version
Uri Wilensky almost 9 years ago Updated from NetLogo 4.1 Download this version
Uri Wilensky almost 9 years ago Updated from NetLogo 4.1 Download this version
Uri Wilensky almost 9 years ago Model from NetLogo distribution Download this version