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Open Model Lab
ChallengesSolved 0 of 172 challenges

Pick a bounded task, then open the exact concept bench that can solve it.

Use this page when you want a concrete next move instead of open browsing. Filters stay on canonical topics, tracks, depth, and progress while the visible labels localize cleanly.

Start with Short-period matchBrowse starter paths
Best first challengeTo tryCore

Short-period match

Starting from Calm start, make the oscillator complete a shorter cycle without turning it into a wider swing. Keep the displacement graph open so the timing change stays visible.

Simple Harmonic Motion

Not started on this browser yet.

Starter challenge paths

Open these only when you want the next few challenge moves narrowed into one authored path.

Starter track0/10 solved

Motion and Circular Motion

Start with vector components, move into projectile paths, and then use circular motion to understand how velocity can keep changing direction.

Short-period force band is the next best challenge from Uniform Circular Motion.

Starter track0/15 solved

Rotational Mechanics

Start with torque as the turning effect of force, use centre of mass and support region for static balance, then carry the same rotational language into moment of inertia, rolling motion, and angular momentum.

Zero turn at the handle is the next best challenge from Torque.

Starter track0/12 solved

Gravity and Orbits

Start with one source mass creating a field and potential well, then use that same gravity model to explain circular speed, orbital periods, and the escape threshold.

Keep the heavier source circular is the next best challenge from Circular Orbits and Orbital Speed.

Show 16 more starter paths
Starter track0/6 solved

Oscillations and Energy

Build from one clean oscillator to energy exchange and then to driven resonance, so the same system grows without changing its core ideas.

Starter track0/10 solved

Fluid and Pressure

Start with pressure in a resting fluid, then carry that same branch through continuity, Bernoulli, buoyancy, and drag-limited motion.

Starter track0/19 solved

Waves

Use oscillation as the entry point, lock down wave speed and wavelength, carry that into longitudinal sound and pitch-versus-loudness cues, add beats as the nearby-frequency superposition bridge, then move into Doppler shifts, interference, standing-wave patterns, and open-vs-closed air-column resonance without losing the live connection between motion and graph.

Starter track0/8 solved

Thermodynamics and Kinetic Theory

Start with temperature-versus-internal-energy bookkeeping, reuse that particle story for gas pressure, then follow energy transfer into heating curves and phase-change shelves.

Starter track0/7 solved

Electricity

Start with source charges and voltage, then carry that same circuit story into current, power, branch behavior, and equivalent resistance.

Starter track0/6 solved

Magnetism

Start with current-made magnetic fields, turn changing flux into induced emf with Faraday and Lenz, and then reuse that same field direction story to explain magnetic force on charges and currents.

Starter track0/11 solved

Sound and Acoustics

Stay on the sound branch long enough that longitudinal motion, pitch-versus-loudness cues, beats, Doppler shifts, and open-vs-closed air-column resonance feel like one acoustics path instead of isolated pages.

Starter track0/10 solved

Wave Optics

Follow the bounded wave-optics branch from polarization into diffraction, double-slit interference, color-dependent refraction, and imaging limits so the newer optics pages read like one compact path instead of isolated stops.

Starter track0/10 solved

Modern Physics

Follow the bounded modern-physics branch from threshold emission into line spectra, matter waves, the Bohr hydrogen model, and half-life so the new concept set reads like one path instead of five isolated pages.

Starter track0/6 solved

Functions and Change

Keep the first math path compact: read parent-curve moves first, then rational asymptotes and domain breaks, then exponential growth and decay, local slope, visible limit behavior, and finally accumulation so change stays graph-first all the way through.

Starter track0/6 solved

Complex and Parametric Motion

Start with complex numbers as points on one plane, turn that plane into unit-circle and polar-coordinate geometry, deepen that same bench into trig identities and inverse-angle reasoning, then carry the coordinate language into motion traced from x(t) and y(t).

Starter track0/4 solved

Vectors and Motion Bridge

Start with vectors as geometric objects on a 2D plane, then carry the same component language into the existing motion-facing vectors bench.

Starter track0/4 solved

Rates and Equilibrium

Start with successful collisions setting reaction rate, then reuse the same chemistry language inside a reversible system that re-balances after a disturbance.

Starter track0/3 solved

Stoichiometry and Yield

Start with one visible reaction recipe, use the lower batch cap to identify the limiting reagent, and then compare actual output with the same theoretical marker.

Starter track0/6 solved

Solutions and pH

Start with concentration in one beaker, add solubility limits and saturation, then reuse that same solution language to read pH, buffers, and neutralization.

Starter track0/5 solved

Algorithms and Search Foundations

Start with visible list work, reuse that search language for binary search, and then carry the branch into one live graph bench for adjacency, BFS, DFS, and visited-state behavior.

Challenge browser

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Showing 19 of 172 challenge entries. Active filters: Waves.

Challenge depth

Core

10 prompts in this depth

OscillationsTo tryCore

Short-period match

Starting from Calm start, make the oscillator complete a shorter cycle without turning it into a wider swing. Keep the displacement graph open so the timing change stays visible.

Simple Harmonic Motion

Path: Oscillations and Energy, Waves

Match3 checks
Open challengeNot started on this browser yet.
WavesTo tryCore

One-cycle probe lag

Starting from Baseline, move the probe until it sits one wavelength downstream: same phase shape, one full cycle later.

Wave Speed and Wavelength

Path: Waves

Condition4 checks
Open challengeNot started on this browser yet.
WavesTo tryCore

Faster wave, same spacing

From Baseline, keep the crest spacing at 1.6 m and raise the wave speed until the source cycles faster and the probe delay shrinks.

Wave Speed and Wavelength

Path: Waves

Condition5 checks
Open challengeNot started on this browser yet.
SoundTo tryCore

Tune slow pulses

Starting near unison, tune the source pair until the envelope pulses at about 0.2 Hz while the source amplitude stays near the baseline.

Beats

Path: Waves, Sound and Acoustics

Match5 checks
Open challengeNot started on this browser yet.
Show 6 more core challenges
SoundTo tryCore

Remove the beat without muting

Starting near unison, make the loud-soft beat disappear while keeping the source amplitude near the baseline.

Beats

Path: Waves, Sound and Acoustics

Match5 checks
Open challengeNot started on this browser yet.
WavesTo tryCore

Higher pitch ahead

Keep the emitted tone near 1.1 Hz and tune the live setup so the observer clearly hears a higher pitch on the moving-source bench.

Doppler Effect

Path: Waves, Sound and Acoustics

Target6 checks
Open challengeNot started on this browser yet.
SoundTo tryCore

Find a strong compression

Starting from Baseline, move the probe until it sits inside a strong compression while the probe-pressure graph and compression overlay stay visible.

Sound Waves and Longitudinal Motion

Path: Waves, Sound and Acoustics

Condition4 checks
Open challengeNot started on this browser yet.
WavesTo tryCore

Find a dark band

Starting from Center bright, move the probe onto a dark region where the screen intensity almost vanishes.

Wave Interference

Path: Waves

Condition3 checks
Open challengeNot started on this browser yet.
WavesTo tryCore

Probe on a node

Starting from the third harmonic, move the probe onto a node so the local oscillation envelope collapses almost to zero.

Standing Waves

Path: Waves

Condition4 checks
Open challengeNot started on this browser yet.
SoundTo tryCore

Closed-end stillness

Starting from the closed-pipe third harmonic, move the probe onto the closed wall so parcel motion nearly disappears while the pressure cue stays strong.

Resonance in Air Columns / Open and Closed Pipes

Path: Waves, Sound and Acoustics

Condition5 checks
Open challengeNot started on this browser yet.

Challenge depth

Stretch

9 prompts in this depth

OscillationsTo tryStretch

Compare the timing

Use compare mode to keep a calm baseline in Setup A and make Setup B cycle faster while both setups keep about the same swing size.

Simple Harmonic Motion

Path: Oscillations and Energy, Waves

Condition5 checksCompare mode
Open challengeNot started on this browser yet.
SoundTo tryStretch

Same beat, lower carrier

Enter compare mode and make Setup B keep the same beat frequency as Setup A while clearly lowering the average carrier frequency.

Beats

Path: Waves, Sound and Acoustics

Match6 checksCompare mode
Open challengeNot started on this browser yet.
WavesTo tryStretch

Lower behind, higher ahead

Enter compare mode and make Setup A hear a lower pitch than emitted while Setup B hears a higher pitch, with both sources keeping the same emitted frequency.

Doppler Effect

Path: Waves, Sound and Acoustics

Match8 checksCompare mode
Open challengeNot started on this browser yet.
SoundTo tryStretch

Louder, same pitch

Enter compare mode and make Setup B louder than Setup A while keeping the pitch the same.

Pitch, Frequency, and Loudness / Intensity

Path: Waves, Sound and Acoustics

Match8 checksCompare mode
Open challengeNot started on this browser yet.
Show 5 more stretch challenges
SoundTo tryStretch

Higher, same loudness cue

Enter compare mode and make Setup B higher in pitch than Setup A while keeping the amplitude and intensity cue matched.

Pitch, Frequency, and Loudness / Intensity

Path: Waves, Sound and Acoustics

Match9 checksCompare mode
Open challengeNot started on this browser yet.
SoundTo tryStretch

One wavelength later

Enter compare mode and keep Setup B one full wavelength farther downstream than Setup A so both probes share the same phase relation but Setup B arrives one cycle later.

Sound Waves and Longitudinal Motion

Path: Waves, Sound and Acoustics

Match8 checksCompare mode
Open challengeNot started on this browser yet.
WavesTo tryStretch

Bright zero crossing

From Center bright, pause at a moment when the combined amplitude is still large but the instantaneous probe displacement has crossed through zero.

Wave Interference

Path: Waves

Condition4 checksInspect time
Open challengeNot started on this browser yet.
WavesTo tryStretch

Center zero crossing

From the fundamental mode, keep the probe at the center antinode and pause right as that antinode crosses through zero displacement.

Standing Waves

Path: Waves

Condition5 checksInspect time
Open challengeNot started on this browser yet.
SoundTo tryStretch

Same slider, different harmonic family

Enter compare mode, keep both setups at the same tube length and the same resonance-order slider setting of 2, then make Setup B the closed-open tube so Setup A lands on the 2nd harmonic while Setup B lands on the 3rd harmonic at a lower frequency.

Resonance in Air Columns / Open and Closed Pipes

Path: Waves, Sound and Acoustics

Match10 checksCompare mode
Open challengeNot started on this browser yet.