Overview
A Mass-Spring System models elastic structures by applying forces based on how far each spring is stretched or compressed from its rest length.
CoreSource checked
Mass-Spring System
Simulates connected particles using spring forces between neighboring masses.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Simulation
- Difficulty
- Intermediate
- Family
- Particle Simulation
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 3
- Code example
- Ready
- Visualization
- Ready
Core Concepts
spring forcerest lengthparticle massdamping
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(springs)
Average
O(steps * springs)
Worst
O(steps * springs)
Space
O(particles + springs)
When to Use
- Use when elastic connections can approximate the simulated material.
- Use when cloth prototypes is a central requirement.
When Not to Use
- Avoid when physically accurate continuum mechanics is required.
- Avoid when the timestep, constraints, or stability requirements exceed what the method can handle.
What It Does
- Stores masses and springs
- Computes elastic spring forces
- Integrates particle motion
Use Cases
- Cloth prototypes
- Soft-body effects
- Educational physics simulation
Inputs
- Particle positions
- Spring connections
- Rest lengths
- Stiffness
Outputs
- Updated particle positions and velocities
Key Formulas (1)
Hooke's law
force = −stiffness · (currentlength − restlength)
force = -stiffness * (current_length - rest_length)Computes the restoring force along a spring.
Pseudocode
- 1.For each spring, measure current length
- 2.Compute force from stretch or compression
- 3.Add equal and opposite forces to connected masses
- 4.Integrate particle velocities and positions
Canonical Example
- Input
- two particles connected by rest length 1, current length 1.2
- Output
- spring pulls particles together
- Explanation
- The stretched spring creates a restoring force.
Implementation Notes
- Add damping and clamp timesteps before increasing spring stiffness.
- Keep units, timestep size, and state variables explicit in tests.
- Keep a tiny example with expected output beside the implementation.
Common Pitfalls
- High stiffness with explicit integration can explode numerically.
- Large timesteps can add energy, damp motion, or make constraints explode.
- Not defining boundary, empty, or degenerate inputs before implementation.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryShow particles connected by springs stretching and pulling back toward rest length.
Step 1 of 4: For each spring, measure current length
simulation-stateNotes
Stiff springs usually require small timesteps or implicit methods.
Sources (1)
What each reference supports for this entry.
Physically Based Modeling
DocumentationSIGGRAPH course notes covering integration, particles, constraints, and rigid-body simulation.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageUsed byCloth Simulation
Cloth simulations often model fabric as a mass-spring network.
Often paired withVerlet Integration
Mass-spring systems are commonly integrated with simple time steppers.
Related Algorithms
Tags
SimulationPhysicsSpring SystemParticles