video/.claude/skills/manimgl-best-practices/references/spring_mass_system.md

Spring-Mass System - Reference Guide

Example file: examples/spring_mass_system.py

User Query Scenarios

This example addresses queries like:

• "Create a spring animation with oscillation"
• "Show damped harmonic motion"
• "Visualize physics simulation with a mass on a spring"
• "Animate a spring-mass system with real-time graph"
• "Compare different damping coefficients"

Scene Thinking Process (3b1b Style)

1. Identify the Core Concept

Damped Harmonic Motion: A mass attached to a spring oscillates, with amplitude decreasing over time due to friction/damping. The equation is: x'' = -kx - μv

2. Visual Design Decisions

Why a parametric helix for the spring?

• Looks realistic with 3D coils
• Stretches naturally when mass moves
• Uses ParametricCurve for smooth rendering

Why track position on a number line?

• Gives quantitative feedback
• Shows exact displacement values
• Easy to understand motion direction

3. Technical Implementation

Creating a Self-Contained Physics Component

class SpringMassSystem(VGroup):
    def __init__(self, x0=0, v0=0, k=3, mu=0.1, ...):
        # Store physics state
        self.k = k
        self.mu = mu
        self.velocity = v0

        # Add physics updater
        self.add_updater(lambda m, dt: m.time_step(dt))

Key insight: Encapsulate physics + visuals in one VGroup subclass. This makes it reusable and keeps animation code clean.

Physics Integration (Euler Method)

def time_step(self, delta_t, dt_size=0.01):
    state = [self.get_x(), self.velocity]
    for _ in range(sub_steps):
        x, v = state
        acceleration = -self.k * x - self.mu * v
        state[0] += v * true_dt
        state[1] += acceleration * true_dt

Dynamic Velocity/Force Vectors

def get_velocity_vector(self, scale_factor=0.5, color=GREEN):
    vector = Vector(RIGHT, fill_color=color)
    vector.add_updater(lambda m: m.put_start_and_end_on(
        self.mass.get_center(),
        self.mass.get_center() + scale_factor * self.velocity * RIGHT
    ))
    return vector

4. Scene Variants

Scene	Purpose
SpringMassDemo	Basic oscillation with velocity/force vectors
SpringWithGraph	Real-time x(t) graph using TracedPath
MultipleSprings	Compare different damping values

Key Patterns Demonstrated

Pattern: Pausable Physics

def pause(self):
    self._is_running = False

def unpause(self):
    self._is_running = True

Pattern: TracedPath for Graphs

tracking_point = Point()
tracking_point.add_updater(lambda p: p.move_to(
    axes.c2p(time_tracker.get_value(), spring.get_x())
))
position_graph = TracedPath(tracking_point.get_center, stroke_color=BLUE)

Run Commands

# Basic demo
manimgl spring_mass_system.py SpringMassDemo -w

# With real-time graph
manimgl spring_mass_system.py SpringWithGraph -w

# Compare damping
manimgl spring_mass_system.py MultipleSprings -w