What is the Pendulum Lab multi-solver?

Pendulum Lab is a guided workflow that chains 2 individual PolySim solvers into one end-to-end analysis, piping each result into the next step.

Yes. Every step runs entirely in your browser using real numerics — no install, no account, no cloud cost. Custom or private solver packs are available as a paid service.

Physics & Quantum Pack · Multi-Solver

Pendulum Lab

Simple to chaotic. This multi-solver chains 2 solvers into a single guided workflow — run each step in order and carry the result forward.

Workflow steps

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Double Pendulum

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Double Pendulum StudioLive

chaotic dynamics · RK4

Controls

Speed1×

Tiny changes in the start explode into totally different motion — deterministic chaos. Drag either bob to set a new starting position; it pauses playback automatically.

Presets

Lower bob mass

Gravity g

▶ Run in Python

Data Inspector

IntegratorRK4

SystemChaotic

DOF2

Lower bob mass10

Gravity g9.8

Governing equation

\ddot{θ}_{1} \ddot{θ}_{2} = \frac{- g ( 2 m _{1} + m _{2} ) sin θ _{1} - m _{2} g sin ( θ _{1} - 2 θ _{2} ) - 2 m _{2} sin ( θ _{1} - θ _{2} ) ( θ ˙ _{2}^{2} L _{2} + θ ˙ _{1}^{2} L _{1} cos ( θ _{1} - θ _{2} ) )}{L _{1} ( 2 m _{1} + m _{2} - m _{2} cos ( 2 θ _{1} - 2 θ _{2} ) )} = \frac{2 sin ( θ _{1} - θ _{2} ) ( θ ˙ _{1}^{2} L _{1} ( m _{1} + m _{2} ) + g ( m _{1} + m _{2} ) cos θ _{1} + θ ˙ _{2}^{2} L _{2} m _{2} cos ( θ _{1} - θ _{2} ) )}{L _{2} ( 2 m _{1} + m _{2} - m _{2} cos ( 2 θ _{1} - 2 θ _{2} ) )} m_{1} = 10, m_{2} = 10, L_{1} = L_{2} = 1.2, g = 9.8

Reading this result: Starting both arms at 90° (π/2) with lower-bob mass 10 and g 9.8 puts the pendulum firmly in its chaotic regime. Unlike a small-angle swing, which would be near-periodic, here trajectories that differ by 0.02 rad diverge exponentially — a positive Lyapunov exponent.

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

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Standing Waves

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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.

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Frequently asked questions

What is the Pendulum Lab multi-solver?: Pendulum Lab is a guided workflow that chains 2 individual PolySim solvers into one end-to-end analysis, piping each result into the next step.
Is it free to use?: Yes. Every step runs entirely in your browser using real numerics — no install, no account, no cloud cost. Custom or private solver packs are available as a paid service.