Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Students · Spring-Mass Systems

Spring-Mass Systems for a water rocket

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a water rocket live below — adjust the inputs and watch it respond, right in your browser.

Cloth

open full solver →

Cloth / Spring-Mass StudioLive

Verlet integration · constraint relaxation

Controls

Speed1×

A grid of masses linked by springs, pinned at the top. Grab any node and drag it around — it's a real Verlet cloth simulation.

Presets

Gravity

Wind

▶ Run in Python

Data Inspector

Nodes28×20

IntegratorVerlet

Constraintsdistance (×3/frame)

Governing equation

x^{'} = 2 x - x_{p r e v} + a Δ t^{2}, ∣ p_{i} - p_{j} ∣ = 16

Reading this result: No wind, so the cloth hangs straight down from its pinned top row and settles into a smooth catenary once the motion damps out.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

↓

Standing Waves

open full solver →

Standing Waves on a StringLive

harmonics · nodes & antinodes

Controls

Speed1×

A string fixed at both ends can only vibrate at its harmonics. Each mode n has n+1 nodes (pink) that stay still while the antinodes swing — the physics of every stringed instrument.

Presets

Harmonic n

Fundamental (Hz)

Amplitude (cm)

▶ Run in Python

Data Inspector

Harmonicn = 3

Frequency330 Hz

Nodes4

Antinodes3

Wavelength2L/3

Governing equation

y = 2 A sin (k x) cos (ω t), f_{3} = \frac{3 v}{2 L} = 330 Hz

Reading this result: 3 half-wavelengths fit the string, so there are 3 antinodes (max swing) and 4 nodes (fixed points). At harmonic n = 3 the string sings at 330 Hz — exactly 3× the 110 Hz fundamental, and the wavelength is 2L/3.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

Also for:Researchers Educators Engineers Hobbyists & Makers K-12 Students First Responders General version →

More with Spring-Mass Systems

Spring-Mass Systems for a projectile from a cannon Spring-Mass Systems for a bouncing ball Spring-Mass Systems for a pendulum clock Spring-Mass Systems for a car braking Spring-Mass Systems for a roller-coaster loop Spring-Mass Systems for a satellite orbit Spring-Mass Systems for a mass on a spring Spring-Mass Systems for a skydiver's free fall

Frequently asked questions

Is this good for students?: Yes — this version of "Spring-Mass Systems for a water rocket" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.