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Concept module

Simple Harmonic Motion

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

Interactive lab

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Starter track

Step 1 of 30 / 3 complete

Oscillations and Energy

Next after this: Oscillation Energy.

1. Simple Harmonic Motion2. Oscillation Energy3. Damping / Resonance

This concept is the track start.

Also in Waves.

See next concept

Why it behaves this way

Explanation

Simple harmonic motion is the cleanest place to see how a restoring effect creates repeating motion. The system keeps trying to return to equilibrium, but it overshoots, so the pattern loops instead of settling immediately.

In Open Model Lab, the goal is not to memorize a formula first. The simulation shows the object, the graph, and the derived quantities together so you can connect amplitude, phase, and angular frequency to what the system is actually doing.

Key ideas

01The object moves fastest near equilibrium and slows near the turning points.
02Acceleration always points back toward equilibrium, not toward where the object is already moving.
03Changing phase shifts the whole pattern without changing the overall shape.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough
Solve the exact state currently on screen. The steps update from the real controls and the current inspected time unless you freeze them.

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Frozen valuesFrozen at 0.00

Using the current state, what is the displacement of the oscillator at ?

Time

0 s

Amplitude

1.4 m

Angular frequency

1.8 rad/s

Phase

0 rad

1. Identify the relation

Use the live displacement relation .

2. Substitute the current values

.

3. Compute the phase angle

The current phase angle is , so the displacement becomes .

Current displacement

The displacement is positive, so the oscillator is on the positive side of equilibrium and the restoring acceleration points back toward the center.

Common misconception

A larger amplitude means the object moves faster at every point.

Amplitude changes the size of the oscillation, but speed still depends on position within the cycle.

Near equilibrium the speed is greatest, while the turning points are where the speed drops to zero.

Mini challenge

If you keep the amplitude the same but double the angular frequency, what changes most clearly on the graphs?

Make a prediction before you reveal the next step.

Predict whether the object travels farther or just cycles faster.

Check your reasoning against the live bench.

The oscillation cycles faster, but the amplitude stays the same.
A larger angular frequency means more cycles per second, so the period shrinks. The turning points stay at the same displacement because amplitude did not change.

Quick test

Variable effect

Question 1 of 4

Use the motion, graph, and equation meaning together. Each question checks whether you can explain what the system must be doing.

If amplitude stays fixed and angular frequency increases, what must change first in the stage and displacement graph?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows a single oscillator moving back and forth across an equilibrium point. The object position, velocity direction, and acceleration direction are linked to the same motion so the relationship stays readable without needing to decode the graph alone.

When the user changes amplitude, angular frequency, or phase, the motion updates immediately and the graph follows the same cycle.

Graph summary

The graphs show displacement, velocity, acceleration, and energy as separate views of the same oscillation.

Each plot makes one part of the cycle obvious so the user can compare phase shifts, turning points, and equilibrium crossings.