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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.
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:
data: URIs are fine.localStorage, sessionStorage, cookies or indexedDB — sandboxed frame, they throw.html block.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.
Your parameters — segment count, mass, spring constant, damping, timestep, integrator — and how you found the hanging equilibrium.
The single fenced html block.
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.
In the first few hundred milliseconds the top end will move immediately and the bottom end will not. At the instant of release the top mass loses the upward support force but still has gravity plus the tension of the stretched upper springs pulling downward, so it begins to accelerate downward strongly — about (41g) for the 41-mass chain used here. The bottom mass, by contrast, starts with the upward tension of its upper spring exactly balancing its weight, and no local force on it changes until the release disturbance propagates down the chain through neighbour springs. With the chosen stiffness and mass, that compression/release wave takes roughly (0.35)–(0.45) s to traverse the 40 segments. So the bottom should sit on the marker line while the top collapses downward, and only after about (0.4) s of simulated time should the bottom begin to drop below the marker.
<!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>
:root { color-scheme: dark; }
* { box-sizing: border-box; }
body {
margin: 0;
font-family: system-ui, -apple-system, "Segoe UI", Roboto, sans-serif;
background: radial-gradient(1200px 800px at 50% -10%, #141b28, #0a0d13);
color: #e9eff8;
display: flex;
flex-direction: column;
align-items: center;
}
header { padding: 16px 16px 4px; text-align: center; }
h1 { margin: 0; font-size: 22px; font-weight: 650; letter-spacing: 0.02em; }
.sub { margin: 4px 0 0; font-size: 13px; color: #9fb0c6; }
#wrap { position: relative; width: min(96vw, 620px); margin: 10px auto; }
canvas {
width: 100%;
height: auto;
display: block;
border-radius: 14px;
background: linear-gradient(180deg, #0b101c, #0d1422 65%, #0b101c);
box-shadow: 0 12px 32px rgba(0,0,0,.45), inset 0 0 0 1px rgba(255,255,255,.05);
}
#hud {
position: absolute; left: 14px; top: 12px;
font-size: 22px; font-weight: 650;
color: #ffd75e; text-shadow: 0 1px 3px rgba(0,0,0,.7);
font-variant-numeric: tabular-nums;
pointer-events: none;
}
#state {
position: absolute; right: 14px; top: 14px;
font-size: 12px; letter-spacing: .08em; text-transform: uppercase;
color: #9fb0c6; text-shadow: 0 1px 2px rgba(0,0,0,.7);
pointer-events: none;
}
.controls {
display: flex; flex-wrap: wrap; gap: 10px; justify-content: center; align-items: center;
padding: 0 14px 8px;
}
button {
appearance: none; border: 1px solid #33455f; background: #1b2536; color: #e9eff8;
padding: 9px 16px; border-radius: 10px; font-size: 14px; font-weight: 600;
cursor: pointer;
}
button:hover:not(:disabled) { background: #243349; }
button:disabled { opacity: .45; cursor: default; }
.panel {
display: flex; align-items: center; gap: 9px;
background: #141c2b; border: 1px solid #2b3a52; border-radius: 10px;
padding: 8px 12px; font-size: 13px; color: #c7d3e5;
}
input[type="range"] { width: 210px; accent-color: #ffd75e; margin: 0; }
#speedVal { min-width: 54px; text-align: right; font-variant-numeric: tabular-nums; }
.note { max-width: 640px; text-align: center; color: #7f92aa; font-size: 12px; padding: 0 16px 18px; }
</style>
</head>
<body>
<header>
<h1>Falling Slinky</h1>
<p class="sub">The top is let go. The bottom does not know until the signal arrives.</p>
</header>
<div id="wrap">
<canvas id="view"></canvas>
<div id="hud">0 ms</div>
<div id="state">hanging</div>
</div>
<div class="controls">
<button id="release">Release</button>
<button id="reset">Reset</button>
<div class="panel">
<label for="speed">Speed</label>
<input id="speed" type="range" min="0.05" max="1" step="0.01" value="1">
<span id="speedVal">1.00×</span>
</div>
</div>
<p class="note">40 spring segments, 41 equal masses. Initial hang is the analytic static equilibrium, not equal spacing.</p>
<script>
(() => {
"use strict";
const canvas = document.getElementById("view");
const ctx = canvas.getContext("2d");
const W = 620;
const H = 780;
const dpr = Math.max(1, Math.min(3, window.devicePixelRatio || 1));
canvas.width = W * dpr;
canvas.height = H * dpr;
ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
// Physical parameters, SI units.
const N = 40; // spring segments
const M = N + 1; // point masses
const MASS = 0.004; // kg per mass
const K = 40.0; // N/m per segment
const REST = 0.020; // m natural length per segment
const DAMP = 0.08; // N s/m internal dashpot per segment
const G = 9.81; // m/s^2
const DT = 1.0e-4; // s fixed physics step
// Drawing scale.
const SUPPORT_Y = 0.12; // m, top support height in world coordinates
const SCALE = 160.0; // px per metre
const CX = W / 2;
const COIL_R = 36.0;
const y = new Float64Array(M);
const v = new Float64Array(M);
const f = new Float64Array(M);
let state = "hanging";
let simTime = 0;
let markerY = null;
let speed = 1;
let accumulator = 0;
let lastFrame = null;
const hud = document.getElementById("hud");
const stateEl = document.getElementById("state");
const releaseBtn = document.getElementById("release");
const resetBtn = document.getElementById("reset");
const speedInput = document.getElementById("speed");
const speedVal = document.getElementById("speedVal");
function hangEquilibrium() {
state = "hanging";
simTime = 0;
accumulator = 0;
markerY = null;
v.fill(0);
y[0] = SUPPORT_Y;
// Static equilibrium:
// Spring between i-1 and i supports masses i..N.
for (let i = 1; i < M; i++) {
const supportedMasses = N - i + 1;
const len = REST + supportedMasses * MASS * G / K;
y[i] = y[i - 1] + len;
}
}
function release() {
if (state !== "hanging") return;
markerY = y[N];
simTime = 0;
accumulator = 0;
state = "free";
}
function reset() {
hangEquilibrium();
}
function physicsStep() {
// Gravity on every mass.
f.fill(MASS * G);
// Spring + internal damping forces between neighbours.
for (let i = 0; i < N; i++) {
const d = y[i + 1] - y[i];
const relV = v[i + 1] - v[i];
const springForce = K * (d - REST) + DAMP * relV;
// Positive force pulls the upper mass down and the lower mass up.
f[i] += springForce;
f[i + 1] -= springForce;
}
// Semi-implicit Euler.
for (let i = 0; i < M; i++) {
v[i] += (f[i] / MASS) * DT;
y[i] += v[i] * DT;
}
simTime += DT;
}
function segmentColor(len) {
const s = (len - REST) / REST;
if (s >= 0) {
// Stretched: pale steel toward warm amber.
const a = Math.min(1, s / 3);
const r = Math.round(214 + 41 * a);
const g = Math.round(220 - 75 * a);
const b = Math.round(235 - 150 * a);
return `rgb(${r},${g},${b})`;
} else {
// Compressed: toward cool blue.
const a = Math.min(1, -s);
const r = Math.round(214 - 85 * a);
const g = Math.round(220 - 25 * a);
const b = 255;
return `rgb(${r},${g},${b})`;
}
}
function draw() {
ctx.clearRect(0, 0, W, H);
// Support beam.
const supportPix = SUPPORT_Y * SCALE;
ctx.save();
ctx.strokeStyle = "#5d6f89";
ctx.lineWidth = 5;
ctx.lineCap = "round";
ctx.beginPath();
ctx.moveTo(CX - 105, supportPix);
ctx.lineTo(CX + 105, supportPix);
ctx.stroke();
ctx.strokeStyle = "#43526a";
ctx.lineWidth = 2;
for (let x = CX - 92; x <= CX + 92; x += 18) {
ctx.beginPath();
ctx.moveTo(x, supportPix);
ctx.lineTo(x + 12, supportPix - 12);
ctx.stroke();
}
ctx.restore();
// Slinky segments.
ctx.save();
ctx.lineCap = "round";
ctx.lineWidth = 3;
for (let i = 0; i < N; i++) {
const y0 = y[i] * SCALE;
const y1 = y[i + 1] * SCALE;
const len = y[i + 1] - y[i];
const midY = (y0 + y1) * 0.5;
const ctrlX = CX + (i % 2 === 0 ? -COIL_R : COIL_R);
ctx.strokeStyle = segmentColor(len);
ctx.beginPath();
ctx.moveTo(CX, y0);
ctx.quadraticCurveTo(ctrlX, midY, CX, y1);
ctx.stroke();
}
// Mass points.
ctx.fillStyle = "rgba(154,171,196,0.9)";
for (let i = 0; i < M; i++) {
ctx.beginPath();
ctx.arc(CX, y[i] * SCALE, 2.1, 0, Math.PI * 2);
ctx.fill();
}
// Bottom end highlight.
ctx.fillStyle = "#ffd75e";
ctx.beginPath();
ctx.arc(CX, y[N] * SCALE