Run Detail
completeddeepseek-v4.1-flashRecorded for these videos
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Provider
openrouter
Challenge Version
v1.0
Turns
1
Duration
204.1s
Total Tokens
51,286
Input Tokens
769
Output Tokens
50,517
Reasoning Tokens
45,191
Reasoning Effort
default
Est. Cost
$0.0304
Started
9/10/2026, 11:10:06 AM
OR Provider
DeepSeek
Finish Reason
stop
Generation ID
gen-1789038606-oNa4fLhvWNlg456xt47Q
Turns (1)
Turn #1
769 in50,517 out45,191 reasoning51,286 total204.1s
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
At the instant the clamp is released, nothing about the slinky's internal forces changes — the springs are still stretched exactly as they were, and every segment above the bottom still feels the weight of everything below it. Only one thing changes: the top segment loses the upward pull that the clamp was applying. So the top segment, which carries the entire weight of the chain above its own weight, kicks downward with acceleration ≈ N·g ≈ 50 g, and it drops roughly a centimetre within the first 10 ms. Every other segment starts with exactly zero acceleration. That disturbance cannot reach the bottom coil faster than one segment per √(m/k) ≈ 7.9 ms, so with 49 gaps the bottom coil must remain exactly at rest — to the last bit of double precision — for the first ≈ 387 ms. It should sit on the marker line, unmoving, while the top of the slinky crumples into it. Around 0.39–0.45 s the compression wave arrives, the bottom coil starts to fall, and from then on the whole thing is a collapsing blob in free fall. Throughout, because the only external force is gravity, the centre of mass must follow ½gt² from t = 0, exactly — the internal forces cancel pairwise and cannot affect it.
The setup
| quantity | value |
|---|---|
| segments | N = 50 (40 is the minimum; 50 gives a nicer coil) |
| segment mass | m = 0.02 kg (total 1.0 kg) |
| gravity | g = 9.8 m/s² |
| spring constant | k = 320 N/m between neighbours |
| unstretched segment | L₀ = 5 mm (natural length 0.25 m) |
| damping | c = 1.0 N·s/m viscous between neighbours (ζ ≈ 0.2 of critical for a single pair — "a little") |
| timestep | Δt = 1×10⁻⁴ s |
| integrator | semi-implicit (symplectic) Euler: v += F/m·Δt; y += v·Δt |
Stability check: the highest chain frequency is ω_max ≈ 2√(k/m) ≈ 253 rad/s, so ω_max·Δt ≈ 0.025 — two orders of magnitude inside the symplectic stability limit of 2. Nothing is clamped, no velocities are capped, no segment is ever frozen after release.
Hanging equilibrium. Solved in closed form, not relaxed into. Spring i (between masses i and i+1) carries the weight of the N−1−i masses below it, so its extension is x_i = (N−1−i)·mg/k, and mass i hangs at y_i = Σ_{j<i}(L₀ + x_j). Checking the force balance on each interior mass: k·x_{i−1} − k·x_i − mg = (N−i)mg − (N−1−i)mg − mg = 0 exactly. The top spring stretches 30 mm, the bottom one 0.6 mm — the coils are wide apart at the top and almost touching at the bottom. Total hanging length ≈ 0.995 m. Before release the top mass is held by the clamp (that is the physical setup, not scripting); the moment Release is pressed that constraint is removed and every mass, including the first, is integrated by the identical rule.
I also verified the relaxation route mentally: because the equilibrium is exact, both the pinned and the relaxed dynamics leave the hanging chain bit-for-bit stationary, and the simulation in fact never advances time before 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>
*, *::before, *::after { box-sizing: border-box; }
html, body {
margin: 0; padding: 0; height: 100%; overflow: hidden;
background: #070a0f; color: #dfe7f1;
font-family: ui-monospace, SFMono-Regular, Menlo, Consolas, "Liberation Mono", monospace;
}
body { display: flex; flex-direction: column; }
header {
display: flex; align-items: center; gap: 20px; flex-wrap: wrap;
padding: 9px 16px; border-bottom: 1px solid #161d29; background: #0a0e15;
}
h1 {
margin: 0; font-size: 12px; font-weight: 600;
letter-spacing: .14em; text-transform: uppercase; color: #7fb4ee;
}
.readouts { display: flex; gap: 22px; margin-left: auto; flex-wrap: wrap; }
.readout { font-size: 12px; color: #7d8ba0; white-space: nowrap; }
.readout b { color: #e9f1fb; font-weight: 600; display: inline-block; text-align: right; }
#clock { min-width: 64px; }
#disp { min-width: 64px; }
#stage { position: relative; flex: 1 1 auto; min-height: 260px; }
canvas { display: block; }
#controls {
display: flex; align-items: center; gap: 18px; flex-wrap: wrap;
padding: 10px 16px; border-top: 1px solid #161d29; background: #0a0e15;
}
button {
font: inherit; font-size: 12px; letter-spacing: .08em;
padding: 8px 22px; border-radius: 6px;
border: 1px solid #2b3a50; background: #141c28; color: #dfe7f1;
cursor: pointer; text-transform: uppercase;
}
button:hover:not(:disabled) { background: #1b2534; border-color: #3d5478; }
button:disabled { opacity: .32; cursor: default; }
#release { border-color: #2f6f4f; background: #12261c; color: #8ff0bb; }
#release:hover:not(:disabled) { background: #173525; border-color: #3f9068; }
.slider {
display: flex; align-items: center; gap: 10px; font-size: 12px;
color: #7d8ba0; text-transform: uppercase; letter-spacing: .1em;
}
input[type=range] { width: 180px; accent-color: #4ea1ff; }
#speedVal { color: #e9f1fb; min-width: 58px; letter-spacing: 0; text-transform: none; }
</style>
</head>
<body>
<header>
<h1>Falling Slinky</h1>
<div class="readouts">
<div class="readout">t = <b id="clock">0.0</b> ms</div>
<div class="readout">bottom coil Δy = <b id="disp">0.0</b> mm</div>
</div>
</header>
<div id="stage"><canvas id="c"></canvas></div>
<div id="controls">
<button id="release">Release</button>
<button id="reset">Reset</button>
<label class="slider" for="speed">speed
<input id="speed" type="range" min="0" max="100" step="1" value="54">
<span id="speedVal">×0.25</span>
</label>
</div>
<script>
(function () {
'use strict';
/* ==================================================================
MODEL
------------------------------------------------------------------
N point masses, mass MASS, joined in series by Hookean springs
(stiffness K, natural length L0) with a viscous element DAMP in
parallel. Gravity G acts on every mass.
While hanging, mass 0 is held by the clamp. On Release the clamp
is removed and *every* mass, 0 included, is evolved by the same
force law. Nothing is pinned, frozen or delayed afterwards.
Hanging equilibrium, solved exactly:
spring i (between mass i and i+1) carries the weight of the
(N-1-i) masses below it, so
x_i = (N-1-i) * MASS * G / K
and mass i sits at y_i = sum_{j<i} ( L0 + x_j ).
Residual force on an interior mass:
K*x_{i-1} - K*x_i - MASS*G
= (N-i)MG - (N-1-i)MG - MG = 0 (identically)
================================================================== */
var N = 50; // segments
var MASS = 0.02; // kg
var G = 9.8; // m/s^2
var L0 = 0.005; // m unstretched segment length
var K = 320; // N/m spring constant between neighbours
var DAMP = 1.0; // N.s/m viscous damping between neighbours
var DT = 1e-4; // s integration step
var MGK = MASS * G / K; // extension produced by one segment's weight
/* ---------------- state ---------------- */
var y = new Float64Array(N);
var v = new Float64Array(N);
var F = new Float64Array(N);
var released = false;
var simTime = 0; // seconds since release
var markerY = 0; // world y of the bottom coil at release
var markerSet = false;
var yBottom0 = 0;
var speed = 0.25;
var acc = 0;
var lastTs = 0;
function setEquilibrium() {
var pos = 0;
for (var i = 0; i < N; i++) {
y[i] = pos;
v[i] = 0;
if (i < N - 1) pos += L0 + (N - 1 - i) * MGK;
}
yBottom0 = y[N - 1];
}
function computeForces() {
var i, f;
for (i = 0; i < N; i++) F[i] = MASS * G;
for (i = 0; i < N - 1; i++) {
f = K * ((y[i + 1] - y[i]) - L0) + DAMP * (v[i + 1] - v[i]);
F[i] += f;
F[i + 1] -= f;
}
}
function step(dt) {
computeForces();
var i;
if (released) {
for (i = 0; i < N; i++) {
v[i] += (F[i] / MASS) * dt;
y[i] += v[i] * dt;
}
simTime += dt;
} else {
/* clamp holds mass 0 -- the physical support, removed on Release */
for (i = 1; i < N; i++) {
v[i] += (F[i] / MASS) * dt;
y[i] += v[i] * dt;
}
y[0] = 0;
v[0] = 0;
}
}
/* ==================================================================
VIEW
================================================================== */
var canvas = document.getElementById('c');
var ctx = canvas.getContext('2d');
var stage = document.getElementById('stage');
var clockEl = document.getElementById('clock');
var dispEl = document.getElementById('disp');
var btnRel = document.getElementById('release');
var btnRes = document.getElementById('reset');
var speedIn = document.getElementById('speed');
var speedLb = document.getElementById('speedVal');
var WORLD_TOP = -0.05;
var WORLD_H = 1.95;
var W = 800, H = 600, cx = 400, scale = 320;
function sy(wy) { return (wy - WORLD_TOP) * scale; }
function resize() {
var r = stage.getBoundingClientRect();
var dpr = Math.min(2, window.devicePixelRatio || 1);
W = Math.max(300, Math.round(r.width));
H = Math.max(240, Math.round(r.height));
canvas.width = Math.round(W * dpr);
canvas.height = Math.round(H * dpr);
canvas.style.width = W + 'px';
canvas.style.height = H + 'px';
ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
scale = H / WORLD_H;
cx = W * 0.5;
}
function coilPoints(pts) {
var AMP = Math.max(9, Math.min(22, scale * 0.045));
pts.length = 0;
for (var i = 0; i < N; i++) {
pts.push(cx + ((i & 1) ? AMP : -AMP), sy(y[i]));
}
return AMP;
}
var _pts = [];
function render() {
/* backdrop */
ctx.fillStyle = '#080b11';
ctx.fillRect(0, 0, W, H);
var grd = ctx.createLinearGradient(0, 0, 0, H);
grd.addColorStop(0, 'rgba(46,74,116,0.32)');
grd.addColorStop(0.55, 'rgba(20,30,46,0.10)');
grd.addColorStop(1, 'rgba(8,11,17,0)');
ctx.fillStyle = grd;
ctx.fillRect(0, 0, W, H);
/* ceiling line + clamp */
var cy = sy(0);
ctx.strokeStyle = 'rgba(110,140,180,0.28)';
ctx.lineWidth = 1;
ctx.beginPath();
ctx.moveTo(0, cy + 0.5);
ctx.lineTo(W, cy + 0.5);
ctx.stroke();
ctx.fillStyle = '#38465c';
ctx.fillRect(cx - 24, cy - 13, 48, 13);
ctx.fillStyle = '#54677f';
ctx.fillRect(cx - 24, cy - 3, 48, 3);
/* marker line */
if (markerSet) {
var my = sy(markerY);
ctx.save();
ctx.setLineDash([9, 7]);
ctx.lineWidth = 1.5;
ctx.strokeStyle = 'rgba(255,176,32,0.85)';
ctx.beginPath();
ctx.moveTo(0, my + 0.5);
ctx.lineTo(W, my + 0.5);
ctx.stroke();
ctx.restore();
ctx.fillStyle = 'rgba(255,176,32,0.92)';
ctx.font = '11px ui-monospace, Menlo, Consolas, monospace';
ctx.textAlign = 'left';
ctx.textBaseline = 'bottom';
ctx.fillText('bottom coil at release', 10, my - 5);
}
/* slinky */
var AMP = coilPoints(_pts);
ctx.lineJoin = 'round';
ctx.lineCap = 'round';
ctx.beginPath();
ctx.moveTo(_pts[0], _pts[1]);
for (var i = 2; i < _pts.length; i += 2) ctx.lineTo(_pts[i], _pts[i + 1]);
ctx.lineWidth = 6.5;
ctx.strokeStyle = 'rgba(110,160,220,0.10)';
ctx.stroke();
var lg = ctx.createLinearGradient(cx - AMP, 0, cx + AMP, 0);
lg.addColorStop(0.0, '#5f7c9e');
lg.addColorStop(0.45, '#d7e8ff');
lg.addColorStop(1.0, '#5f7c9e');
ctx.beginPath();
ctx.moveTo(_pts[0], _pts[1]);
for (var j = 2; j < _pts.length; j += 2) ctx.lineTo(_pts[j], _pts[j + 1]);
ctx.lineWidth = 2.2;
ctx.strokeStyle = lg;
ctx.stroke();
/* bottom coil indicator */
var by = sy(y[N - 1]);
ctx.beginPath();
ctx.arc(cx, by, 4.5, 0, Math.PI * 2);
ctx.fillStyle = '#ff6b6b';
ctx.fill();
}
/* ==================================================================
CONTROLS
================================================================== */
function doReset() {
released = false;
simTime = 0;
markerSet = false;
acc = 0;
setEquilibrium();
btnRel.disabled = false;
clockEl.textContent = '0.0';
dispEl.textContent = '0.0';
render();
}
function doRelease() {
if (released) return;
released = true;
markerY = y[N - 1];
markerSet = true;
simTime = 0;
acc = 0;
btnRel.disabled = true;
}
function applySpeed() {
var t = Number(speedIn.value) / 100; // 0 .. 1
speed = 0.05 * Math.pow(20, t); // 1/20 .. 1/1
speedLb.textContent = '\u00D7' + speed.toFixed(2);
}
btnRel.addEventListener('click', doRelease);
btnRes.addEventListener('click', doReset);
speedIn.addEventListener('input', applySpeed);
/* ==================================================================
LOOP
================================================================== */
function frame(ts) {
if (!lastTs) lastTs = ts;
var dtReal = (ts - lastTs) / 1000;
lastTs = ts;
if (dtReal < 0) dtReal = 0;
if (dtReal > 0.1) dtReal = 0.1;
if (released) {
acc += dtReal * speed;
var n = 0;
while (acc >= DT && n < 8000) { step(DT); acc -= DT; n++; }
if (n >= 8000) acc = 0; /* tab was away; do not catch up forever */
}
render();
clockEl.textContent = (simTime * 1000).toFixed(1);
dispEl.textContent = ((y[N - 1] - yBottom0) * 1000).toFixed(1);
requestAnimationFrame(frame);
}
/* ==================================================================
BOOT
================================================================== */
resize();
window.addEventListener('resize', resize);
if (window.ResizeObserver) new ResizeObserver(resize).observe(stage);
applySpeed();
doReset();
requestAnimationFrame(frame);
})();
</script>
</body>
</html>
What it actually shows
I have not been able to execute this file, so I am separating what is provable from the code from what I am predicting.
Provable, because the code forces it:
- Before Release nothing moves at all. The residual force on every interior mass is algebraically zero, so the hanging state is a genuine fixed point of the discrete equations, not an approximation to one. The visitor will see the correct non-uniform hanging shape — wide gaps up top, tight coils at the bottom — and it will be perfectly still.
- The centre of mass follows ½gt² exactly, from t = 0. In
computeForcesthe internal termfis added toF[i]and subtracted fromF[i+1]from the same variable, so the pairwise cancellation is exact in floating point and the total force is identically N·m·g at every step. The CM therefore cannot lag or lead free fall, regardless of how the springs behave. - The bottom coil is exactly motionless for a long time. Its acceleration depends only on
y[N−2]andv[N−2]; those in turn depend on mass N−3, and so on. In the continuous-time linear chain the response at the far end of 49 stages is a Bessel function whose argument only reaches its turning point at t = 49·√(m/k) = 49 × 7.9 ms ≈ 387 ms. Below that the response is smaller than double-precision noise. So thebottom coil Δyreadout should sit at0.0 mm— genuinely 0.0, not "small" — until roughly 390 ms, then start climbing. If you see the bottom coil drifting before ~380 ms, my model of the causality is wrong and I want to know.
Not provable without running it, and where I would put my money on being wrong:
- The exact arrival time. The rigorous lower bound is 387 ms; the free-flow estimate using the continuum wave speed √(T/μ) summed over segments gives ≈ 490 ms, because near the bottom the coil spacing approaches the unstretched length and the continuum speed collapses. I genuinely do not know which of those the discrete chain will follow, because the fast, low-amplitude precursor and the slow, energy-carrying part of the wave arrive at different times. My honest prediction is that the bottom coil is still on the marker line at 380 ms, has moved less than a millimetre at 450 ms, and is visibly falling by 600 ms. If it turns out to sit still for 600 ms or more, the continuum estimate wins and my 387 ms number was a red herring.
- What happens after the collapse is not like a real slinky. This is the one place where I know the model is unfaithful, and I want to say so plainly rather than defend it. I used linear Hookean springs in both directions, exactly as instructed, which means the coils push back when the slinky compresses past its 0.25 m natural length. The stored spring energy at release is ≈ 2.4 J (about a third of the gravitational energy released), and in a lossless linear chain that becomes relative motion between coils of order 2 m/s — the collapse will overshoot, the coils will visibly pass through one another on the way back, and the slinky will keep breathing and jiggling as it falls. A real slinky does not do this: its coils collide inelastically and the thing collapses into a compact blob. The damping (ζ ≈ 0.2) takes the edge off the high-frequency jitter within a few tens of milliseconds, but it cannot remove the energy stored in the low modes, and those decay with a time constant of order a second. So expect a livelier, springier aftermath than the Veritasium video. That is a known, acknowledged failure of the linear-spring model, not a numerical one.
- Nothing else is fiddled. No velocity clamping, no terminal-velocity cap, no re-pinning, no per-segment special cases after Release. If you want to check the integrator is clean, watch the
bottom coil Δyreadout after the slinky has fallen off the bottom of the canvas: it should keep growing smoothly as ½gt², with no jumps.
Attachments
deepseek/deepseek-v4.1-flash — page