Simple Pendulum Simulator
Classroom worksheet · Interactive simulation: https://lkforge.com/tools/physics/simple-pendulum/
Name: Date:
Learning objectives
- Determine what the period of a pendulum depends on.
- Apply the small-angle period formula.
- Recognize the independence of period from mass and amplitude (small angles).
Variables to change
- Length
- Gravity
- Initial angle
- Mass
Procedure
- Time the period at a fixed length and small angle.
- Double the length and time the period again.
- Change the mass (same length, small angle) and time the period.
- Increase the starting angle to a large value and note any change.
Observations
Record the period for each length, mass, and starting angle.
Questions
- What happened to the period when you doubled the length?
- Did changing the mass change the period?
- Write the small-angle period formula.
- For small swings, does amplitude affect the period?
- What happens to the period at large starting angles?
Answer key (instructors)
- 1. It increased by a factor of √2, because T ∝ √L.
- 2. No — for a simple pendulum the period is independent of mass.
- 3. T = 2π·√(L/g).
- 4. Almost not at all; the small-angle approximation makes the period independent of amplitude.
- 5. The period grows slightly longer than the small-angle formula predicts, because the approximation breaks down.
A simple pendulum’s period T = 2π√(L/g) depends on length and gravity, not mass, and is nearly independent of amplitude for small swings. At large angles the small-angle approximation fails and the period lengthens.