Run Detail
completedcrouton-alphaRecorded for this video
Provider
openrouter
Challenge Version
v1.0
Turns
1
Duration
48.3s
Total Tokens
2,966
Input Tokens
758
Output Tokens
2,208
Reasoning Tokens
267
Reasoning Effort
max
Est. Cost
$0.0000
Started
11/3/2026, 9:43:56 PM
OR Provider
Stealth
Finish Reason
stop
Generation ID
gen-1793742236-zfzY7nBbWE0cvuyynxSG
Turns (1)
Turn #1
758 in2,208 out267 reasoning2,966 total48.2s
user
You build physics demonstrations for a science museum. The exhibits have to be right, because there is usually a physicist in the room.
Build me the falling slinky.
The exhibit
A single HTML page. A slinky — at least 40 coupled segments — hangs from a fixed point at the top of the canvas, at rest, under gravity. Then it is released.
Controls:
- Release — lets go of the top. Reset — hangs it back up, at rest.
- A speed slider from full speed down to about 1/20th, so a visitor can watch the interesting part.
- A marker line drawn across the canvas at the height of the bottom of the slinky at the instant of release, staying where it was put. Visitors need something to compare against.
- A running clock in milliseconds since release.
The physics, and I will be checking it
- Model it properly: masses connected by springs, with gravity and a little damping. Hooke's law between neighbours, integrated over small time steps.
- The hanging state must be the true equilibrium. A real slinky at rest is not evenly spaced — the coils near the top carry the weight of everything below them and are stretched further apart than the coils at the bottom. Your initial condition must have this. Solve for it or relax into it, but do not start from even spacing and call it hanging.
- The integrator must be stable at the stiffness you choose. If it explodes, lower the stiffness or shorten the step — do not add a fudge factor that clamps velocities and hides it.
- No scripted behaviour. Every segment obeys the same rules. Nothing is pinned, frozen, delayed or special-cased once you press Release. If any segment is treated differently from its neighbours at any point after release, that is scripting, and you must say so.
House rules
- One file. Everything inline — no CDN, no external stylesheet, font, script or image.
data:URIs are fine. - No libraries. No physics engine.
- No network at runtime.
- No
localStorage,sessionStorage, cookies orindexedDB— sandboxed frame, they throw. - Return the file as exactly one fenced
htmlblock.
Answer in exactly these sections
The prediction
Before the file, and before you write it. In one paragraph: what will this simulation show in the first few hundred milliseconds after release, and why does the physics require that? Be concrete about what each end of the slinky does and roughly when.
Commit to this. It is the claim I am going to test your simulation against.
The setup
Your parameters — segment count, mass, spring constant, damping, timestep, integrator — and how you found the hanging equilibrium.
The file
The single fenced html block.
What it actually shows
Now be honest. Having written it, does the simulation reproduce what you predicted?
Say plainly if it does not. Say if you are unsure. Say if it only works at some parameter settings and falls apart at others.
Do not tell me it shows the right thing because the physics says it should. I am going to open the file, press Release, and watch it against the marker line. If your prediction and your simulation disagree, the answer I want is the one that says so — that is a working scientist noticing their model is wrong, and it scores far above a confident write-up of a result the code does not produce.
assistant
The prediction
After release the bottom end will remain essentially at the marker line, moving less than a pixel, for roughly 250–350 ms while the top end immediately plunges downward, accelerating faster than g, and the slinky shortens dramatically from the top down as the stretched upper springs relax and the coils pile up toward the still-stationary bottom, after which the bottom will finally begin to fall and the compacted slinky will fall roughly together; this must happen because in the hanging equilibrium each spring's tension exactly balances the weight below it, so the bottom mass starts with zero net force, whereas the top mass starts with gravity plus the tension of the spring below it pulling it down, and that disturbance can only propagate down the chain at the finite wave speed of the coupled masses and springs, taking a few hundred milliseconds to reach the bottom while the centre of mass accelerates at g throughout.
The setup
- Segments: $N=50$ masses, 49 springs between neighbours. Mass per segment $m=1.0$.
- Springs: $k=20000$, natural length $a_0=0.008\ \text{m}$ per spring, Hooke's law $F=k(L-a_0)$ between neighbours, gravity $g=9.81\ \text{m/s}^2$ downward.
- Damping: spring-relative viscous term $b=4.0$, force $b,(v_{i+1}-v_i)$ on spring $i$. Internal only, no global drag, no velocity clamping or other fudge factor.
- Integrator: semi-implicit Euler with fixed substep $dt=0.0005\ \text{s}$. The speed slider scales real time from $1.00\times$ to $0.05\times$, but the physics substep stays $dt$. $\omega_{\max}\approx2\sqrt{k/m}\approx283\ \text{rad/s}$, so $dt,\omega_{\max}\approx0.14$, well below the stability limit of 2 for this integrator.
- Hanging equilibrium, solved analytically, not evenly spaced and not relaxed from even spacing: spring $i$ counting from the top supports $N-1-i$ masses below it, so its equilibrium spacing is $a_0+(N-1-i)mg/k$, placed cumulatively from the anchor. Top spacing $\approx0.032\ \text{m}$, bottom spacing $\approx0.0085\ \text{m}$, total length $\approx0.99\ \text{m}$. With this spacing every mass except the top has exactly zero net force at rest; the top is held at the anchor before release.
- After Release there is no pinning, freezing, delay or special-casing: the anchor is removed and every segment obeys the identical gravity plus neighbour-spring force law. Reset recomputes the analytic equilibrium and zeroes velocities.
- Display: $500\ \text{px/m}$ on a $640\times720$ canvas, marker line fixed at the initial bottom height, clock showing simulated milliseconds since release.
The file
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Falling Slinky</title>
<style>
body{font-family:system-ui,sans-serif;margin:20px;background:#f7f7f2;color:#222;text-align:center}
canvas{background:#fff;border:1px solid #999;display:block;margin:10px auto;max-width:100%}
.controls{margin:10px 0}
button{font-size:16px;padding:6px 14px;margin:0 4px}
#clock{font-variant-numeric:tabular-nums;font-size:20px;margin-left:16px}
label{margin-left:12px}
</style>
</head>
<body>
<h1>Falling Slinky</h1>
<div class="controls">
<button id="releaseBtn">Release</button>
<button id="resetBtn">Reset</button>
<label>Speed <input id="speed" type="range" min="0.05" max="1" step="0.01" value="1"> <span id="speedVal">1.00×</span></label>
<span id="clock">0 ms</span>
</div>
<canvas id="c" width="640" height="720"></canvas>
<p id="status">Hanging at rest. Press Release.</p>
<script>
(function(){
"use strict";
var N=50;
var m=1.0;
var k=20000.0;
var a0=0.008;
var g=9.81;
var b=4.0;
var dt=0.0005;
var scale=500;
var anchorX=320;
var anchorY=60;
var canvas=document.getElementById('c');
var ctx=canvas.getContext('2d');
var releaseBtn=document.getElementById('releaseBtn');
var resetBtn=document.getElementById('resetBtn');
var speedInput=document.getElementById('speed');
var speedVal=document.getElementById('speedVal');
var clockEl=document.getElementById('clock');
var statusEl=document.getElementById('status');
var y=[];
var v=[];
var released=false;
var simTime=0;
var markerY=0;
function reset(){
y=[]; v=[];
for(var i=0;i<N;i++){ y.push(0); v.push(0); }
y[0]=0;
for(var j=0;j<N-1;j++){
var spacing=a0+(N-1-j)*m*g/k;
y[j+1]=y[j]+spacing;
}
simTime=0;
released=false;
markerY=anchorY+y[N-1]*scale;
statusEl.textContent='Hanging at rest. Press Release.';
clockEl.textContent='0 ms';
releaseBtn.disabled=false;
}
function step(h){
var a=[];
for(var i=0;i<N;i++) a.push(g);
for(var s=0;s<N-1;s++){
var len=y[s+1]-y[s];
var rel=v[s+1]-v[s];
var F=k*(len-a0)+b*rel;
a[s]+=F/m;
a[s+1]-=F/m;
}
for(var q=0;q<N;q++){
v[q]+=a[q]*h;
y[q]+=v[q]*h;
}
}
function draw(){
ctx.clearRect(0,0,canvas.width,canvas.height);
ctx.strokeStyle='#c00';
ctx.lineWidth=2;
ctx.setLineDash([8,6]);
ctx.beginPath();
ctx.moveTo(10,markerY);
ctx.lineTo(canvas.width-10,markerY);
ctx.stroke();
ctx.setLineDash([]);
ctx.fillStyle='#c00';
ctx.font='14px system-ui, sans-serif';
ctx.fillText('initial bottom',14,markerY-8);
ctx.fillStyle='#333';
ctx.fillRect(anchorX-30,anchorY-14,60,10);
ctx.beginPath();
ctx.moveTo(anchorX,anchorY-4);
ctx.lineTo(anchorX-6,anchorY+6);
ctx.lineTo(anchorX+6,anchorY+6);
ctx.closePath();
ctx.fill();
if(!released){
ctx.strokeStyle='#333';
ctx.lineWidth=2;
ctx.beginPath();
ctx.moveTo(anchorX,anchorY+6);
ctx.lineTo(anchorX,anchorY+y[0]*scale);
ctx.stroke();
}
ctx.strokeStyle='#1a5fb4';
ctx.lineWidth=3;
ctx.beginPath();
for(var i=0;i<N;i++){
var px=anchorX;
var py=anchorY+y[i]*scale;
if(i===0) ctx.moveTo(px,py); else ctx.lineTo(px,py);
}
ctx.stroke();
ctx.fillStyle='#1a5fb4';
for(var j=0;j<N;j++){
ctx.beginPath();
ctx.arc(anchorX,anchorY+y[j]*scale,6,0,Math.PI*2);
ctx.fill();
}
ctx.fillStyle='#222';
ctx.font='12px system-ui, sans-serif';
ctx.fillText('top',anchorX+12,anchorY+y[0]*scale+4);
ctx.fillText('bottom',anchorX+12,anchorY+y[N-1]*scale+4);
}
var last=performance.now();
function frame(now){
var realDt=(now-last)/1000;
last=now;
if(realDt>0.05) realDt=0.05;
if(realDt<0) realDt=0;
if(released){
var speed=parseFloat(speedInput.value);
var remaining=realDt*speed;
while(remaining>1e-12){
var h=Math.min(dt,remaining);
step(h);
simTime+=h;
remaining-=h;
}
}
clockEl.textContent=Math.round(simTime*1000)+' ms';
draw();
requestAnimationFrame(frame);
}
releaseBtn.addEventListener('click',function(){
if(!released){
released=true;
releaseBtn.disabled=true;
statusEl.textContent='Released. Watch the bottom against the red marker line.';
}
});
resetBtn.addEventListener('click',reset);
speedInput.addEventListener('input',function(){
var s=parseFloat(speedInput.value);
speedVal.textContent=s.toFixed(2)+'\u00d7';
});
reset();
requestAnimationFrame(frame);
})();
</script>
</body>
</html>
What it actually shows
I have not run this exact file in a browser in this session, so I cannot claim a visual test, and I am not going to claim it works merely because the physics says it should. What I can verify from the code as written is narrower: the analytic equilibrium makes the initial net force zero for every mass except the top, the internal spring and damping forces cancel in the total, so the centre of mass accelerates at $g$, and the fixed $dt$ is in the stable range for the chosen $k$ and $m$ with no clamping. On that basis I expect the bottom to stay within about a pixel of the marker for roughly the predicted few hundred milliseconds, the top to plunge and the length to collapse from the top, and the whole slinky then to fall out of the canvas after roughly $0.6$–$0.8\ \text{s}$ of simulated time. I am unsure of the exact collapse time to better than a few tens of milliseconds, because the linear wave estimate $N/\sqrt{k/m}\approx0.35\ \text{s}$ is not the full nonlinear discrete motion, and a small discrete precursor motion of the bottom before the main collapse cannot be ruled out without running it. Two known mismatches with a textbook continuous slinky should be visible if you test it: the discrete top mass has an initial acceleration of $Ng=50g$ for roughly the first $10\ \text{ms}$ until its spring relaxes, not the continuous $2g$, and the springs have no solid-coil limit, so pile-up is soft compression below $a_0$ rather than hard stacking, with light damping leaving oscillations after collapse. If the bottom in the file moves substantially before about $200\ \text{ms}$, or the top does not plunge immediately, then the prediction above is wrong for this code and should be recorded as such.
Attachments
stealth/crouton-alpha — page