Coordinate representations
Inspect the same quarter-cycle instant on the apparatus and graphs.
AP Physics 1 · Unit 7 · Oscillations
Graphing Spring Simple Harmonic Motion
Connect spring motion to recorded displacement, velocity and acceleration graphs using slope, area and a shared time cursor.
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Learn by doing
Three ideas you’ll put into motion
Measure graph relationships
Use local slopes and signed areas from recorded motion.
Model a new release
Relate period, frequency and sine or cosine models to starting conditions.
The big idea
The key ideas, at a glance.
Graphs describe the same motion
Position slope is velocity; velocity slope is acceleration. Signed area under velocity gives displacement.
Phase describes cycle progress
Frequency is 1/T and angular frequency is 2π/T. A cosine describes release from the positive turning point.
A quick comparison
Compare the positive displacement peak and first negative velocity peak.
The peaks are separated by a quarter cycle.
Teaching this topic?Classroom fit, AP connections, and support
- Classroom fit
- Use for a concept introduction, guided independent practice, or a projected class discussion.
- Before students begin
- Spring SHM, graph slope and area, period and basic trigonometric functions.
- Built-in support
- Prepared scenes, guided prompts, and feedback on lesson questions.
- AP Physics 1 connections
- Unit 7: representations, period, frequency and phase in SHM.
- Check for understanding
- Ask for the initial signs and slopes after release from a negative turning point.
Ready to test your thinking?
The first scene is set up. Start the lesson and explore.