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Follow the authored sequence, or switch to recap mode for a faster review of the same path.

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Starter track3 concepts2 checkpoints80 min

Oscillations and Energy

Not started

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

Stay with one oscillator long enough that the force story, motion story, and energy story all feel like the same system viewed from different angles. This is the compact path for learners who want one model to deepen rather than jump topics too early.

Restoring forceEnergy exchangeResonance

Entry diagnostic

Decide where to enter this path without opening a second testing system.

Use one quick test on simple harmonic motion and the existing energy checkpoint challenge to decide whether to start from the restoring-force basics or jump ahead to driven resonance.

Start from beginning0 / 2 probes ready

See whether the oscillator loop is already secure

Start from beginning

No saved diagnostic checks are available yet, so the opening concept is still the best place to start.

Uses the same local-first quick tests, checkpoint challenges, and track history already saved in this browser.

Begin with Simple Harmonic Motion
  1. Quick testNot started4 questions

    SHM quick test

    Check whether displacement, restoring force, and phase in the core oscillator are already stable.

    No saved quick-test result yet.

    SHM
    Open Simple Harmonic Motion quick test
  2. ChallengeNot started4 checks

    Energy handoff checkpoint

    Use the existing equal-split challenge to confirm that the motion and energy stories still match before resonance takes over.

    No saved checkpoint attempt yet.

    Energy in SHMInspect time
    Open Equal split

Why this order

The sequence is authored to keep the model honest.

Simple harmonic motion establishes the restoring-force loop. Oscillation and energy then reuses that same motion to explain where energy sits and how it trades places, and damping and resonance closes by showing what changes when the oscillator is driven and losses matter.

Shared concept pages

Each step opens the same simulation-first framework.

Compare mode, prediction mode, quick test, worked examples, guided overlays, challenge mode, and read-next cues stay on the concept pages. The track only decides the guided order and the next recommended stop.

Guided path

Follow the concepts and checkpoint moments in order.

Checkpoint cards reuse the authored challenge entries already living on the concept pages.

  1. 1Not startedMastery: NewStart here

    Simple Harmonic Motion

    See one repeating system from displacement to acceleration and back again, with the math tied directly to the motion on screen.

    Start here before moving into Oscillation Energy.

    OscillationsIntro25 min
    Start concept
  2. 2Not startedMastery: New

    Oscillation Energy

    Watch kinetic and potential energy trade places in simple harmonic motion while the total stays fixed by amplitude and spring stiffness.

    Builds on Simple Harmonic Motion before setting up Damping / Resonance.

    OscillationsIntro25 min
    Open concept
  3. Checkpoint 1LockedNot started

    Energy handoff checkpoint

    Pause the oscillator when the motion and the energy graph tell the same half-kinetic, half-potential story.

    Finish Oscillation Energy first. This checkpoint ties together SHM and Energy in SHM through Equal split.

    Pause here after Oscillation Energy before moving into Damping / Resonance.

    SHMEnergy in SHM4 checksStretchInspect timeGraph-linkedGuided start
    Return to Energy in SHMOpen concept
  4. 3Not startedMastery: New

    Damping / Resonance

    Explore how damping removes energy, how driving frequency changes amplitude, and why resonance becomes dramatic near the natural frequency.

    Capstone step after Oscillation Energy.

    ResonanceIntermediate30 min
    Open concept
  5. Checkpoint 2LockedNot started

    Resonance checkpoint

    Close the track by tuning a driven oscillator near resonance instead of treating damping and resonance as a separate formula shelf.

    Finish Damping / Resonance first. This checkpoint ties together SHM, Energy in SHM, and Damping through Lock near resonance.

    Final checkpoint that closes the authored track after Damping / Resonance.

    SHMEnergy in SHMDamping4 checksCoreGraph-linkedGuided start
    Return to DampingOpen concept