From cc35800e6a7459d4a067c0478de8a5c657faf299 Mon Sep 17 00:00:00 2001
From: Tong Mu <dkwingsmt@users.noreply.github.com>
Date: Fri, 21 Mar 2025 13:46:07 -0700
Subject: [PATCH] Fix SpringSimulation formula for underdamping (#165017)

Fix https://github.com/flutter/flutter/issues/163858

## Pre-launch Checklist

- [ ] I read the [Contributor Guide] and followed the process outlined
there for submitting PRs.
- [ ] I read the [Tree Hygiene] wiki page, which explains my
responsibilities.
- [ ] I read and followed the [Flutter Style Guide], including [Features
we expect every widget to implement].
- [ ] I signed the [CLA].
- [ ] I listed at least one issue that this PR fixes in the description
above.
- [ ] I updated/added relevant documentation (doc comments with `///`).
- [ ] I added new tests to check the change I am making, or this PR is
[test-exempt].
- [ ] I followed the [breaking change policy] and added [Data Driven
Fixes] where supported.
- [ ] All existing and new tests are passing.

If you need help, consider asking for advice on the #hackers-new channel
on [Discord].

<!-- Links -->
[Contributor Guide]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#overview
[Tree Hygiene]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md
[test-exempt]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#tests
[Flutter Style Guide]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Style-guide-for-Flutter-repo.md
[Features we expect every widget to implement]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Style-guide-for-Flutter-repo.md#features-we-expect-every-widget-to-implement
[CLA]: https://cla.developers.google.com/
[flutter/tests]: https://github.com/flutter/tests
[breaking change policy]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#handling-breaking-changes
[Discord]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Chat.md
[Data Driven Fixes]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Data-driven-Fixes.md
---
 .../lib/src/physics/spring_simulation.dart    |  2 +-
 .../test/physics/spring_simulation_test.dart  | 33 +++++++++++++++++++
 2 files changed, 34 insertions(+), 1 deletion(-)

diff --git a/packages/flutter/lib/src/physics/spring_simulation.dart b/packages/flutter/lib/src/physics/spring_simulation.dart
index 3f0bc3a519..cc35c0720b 100644
--- a/packages/flutter/lib/src/physics/spring_simulation.dart
+++ b/packages/flutter/lib/src/physics/spring_simulation.dart
@@ -364,7 +364,7 @@ class _UnderdampedSolution implements _SpringSolution {
     final double w =
         math.sqrt(4.0 * spring.mass * spring.stiffness - spring.damping * spring.damping) /
         (2.0 * spring.mass);
-    final double r = -(spring.damping / 2.0 * spring.mass);
+    final double r = -(spring.damping / 2.0 / spring.mass);
     final double c1 = distance;
     final double c2 = (velocity - r * distance) / w;
     return _UnderdampedSolution.withArgs(w, r, c1, c2);
diff --git a/packages/flutter/test/physics/spring_simulation_test.dart b/packages/flutter/test/physics/spring_simulation_test.dart
index 5e27ed6720..48caeec56a 100644
--- a/packages/flutter/test/physics/spring_simulation_test.dart
+++ b/packages/flutter/test/physics/spring_simulation_test.dart
@@ -36,6 +36,39 @@ void main() {
     expect(snappingSimulation.dx(time), 0);
   });
 
+  test('SpringSimulation results are continuous near critical damping', () {
+    // Regression test for https://github.com/flutter/flutter/issues/163858
+    const double time = 0.4;
+    const double stiffness = 0.4;
+    const double mass = 0.4;
+    final SpringSimulation critical = SpringSimulation(
+      SpringDescription.withDampingRatio(stiffness: stiffness, mass: mass),
+      0,
+      1,
+      0,
+    );
+    expect(critical.x(time), moreOrLessEquals(0.06155, epsilon: 0.01));
+    expect(critical.dx(time), moreOrLessEquals(0.2681, epsilon: 0.01));
+
+    final SpringSimulation slightlyOver = SpringSimulation(
+      SpringDescription.withDampingRatio(stiffness: stiffness, mass: mass, ratio: 1 + 1e-3),
+      0,
+      1,
+      0,
+    );
+    expect(slightlyOver.x(time), moreOrLessEquals(0.06155, epsilon: 0.01));
+    expect(slightlyOver.dx(time), moreOrLessEquals(0.2681, epsilon: 0.01));
+
+    final SpringSimulation slightlyUnder = SpringSimulation(
+      SpringDescription.withDampingRatio(stiffness: stiffness, mass: mass, ratio: 1 - 1e-3),
+      0,
+      1,
+      0,
+    );
+    expect(slightlyUnder.x(time), moreOrLessEquals(0.06155, epsilon: 0.01));
+    expect(slightlyUnder.dx(time), moreOrLessEquals(0.2681, epsilon: 0.01));
+  });
+
   group('SpringDescription.withDurationAndBounce', () {
     test('creates spring with expected results', () {
       final SpringDescription spring = SpringDescription.withDurationAndBounce(bounce: 0.3);