Find which oscillator depends on mass, and explain why only one does
Three steps, the way the exam actually works: work through the lab, write down your own measurements, then answer a 9-point free response. What you recorded goes to the grader with your writing, so a conclusion that does not follow from your own numbers will cost you the point — exactly as it would with a real reader.
Predict before you look
- Both a pendulum and a mass on a spring reduce to d²x/dt² = −ω²x. Write down what ω equals for each before you begin.
- For each oscillator, name the force that provides the restoring effect. That answer alone predicts the result of this investigation.
Nothing to submit here — these are to think through, so the prediction below is an informed one rather than a guess.
Commit to an answer now. It is not graded and being wrong costs nothing — the point is to have something specific to reconcile against once you have the data.
Answer every prediction to unlock the lab. A sentence is enough.
Run the investigation
Predictions first
The procedure and the simulation unlock once you have committed above. Observing before predicting is how a wrong intuition survives a lab intact.
Record what you measured
These are your numbers, not ours. The grader sees them, so your conclusions have to follow from what you actually recorded.
| Pendulum period, L = 1.00 m, mass 1.0 kg | s |
|---|---|
| Spring period, k = 20 N/m, mass 1.0 kg | s |
| Pendulum period, mass 2.0 kg | s |
| Spring period, mass 2.0 kg | s |
| Pendulum period, mass 3.0 kg | s |
| Spring period, mass 3.0 kg | s |
| Pendulum period, L = 2.00 m, mass 1.0 kg | s |
| Spring period, k = 5 N/m, mass 1.0 kg | s |
Answer the free response
Using your recorded periods: (a) State what happened to each period as the mass was tripled, citing your six numbers. (b) Explain the difference by writing the equation of motion for each oscillator and identifying where the mass appears. (c) Your spring periods at 1.0 and 2.0 kg differ by a factor you can compute. State that factor and explain why it is not 2. (d) Compare the effect of doubling the pendulum length with the effect of quartering the spring constant, using your last two readings, and explain why both produced similar period changes.
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