Pendulum Oscillation
Visualize the simple pendulum and its harmonic motion. Investigate how length, gravity, and mass affect the period and frequency, complete with real-time energy bar charts.
THE SIMPLE PENDULUM
A simple pendulum consists of a point mass () on a massless string. For small angles (less than 15°), the restoring force is approximately proportional to displacement, resulting in Simple Harmonic Motion. This tool explores the factors that influence the period of a pendulum.
THE SMALL ANGLE APPROXIMATION
The actual restoring force is . For small , (in radians), which makes the force linear and the period independent of amplitude.
HOW TO USE THIS VISUALIZATION
1. **Change Length**: Adjust and watch the period change.\n2. **Adjust Gravity**: Move the pendulum to the Moon or Jupiter.\n3. **Vary Mass**: Observe that mass does NOT change the period.\n4. **Increase Angle**: Push the pendulum beyond 15° and notice the small errors in the period calculation.
CORE FORMULAS
AP EXAM CONNECTION
Unit: Unit 7: Oscillations (Topic 7.1)
Learning Objective: 7.1.1
COMMON MISCONCEPTIONS
- Thinking mass affects the period of a pendulum (it only does for springs).
- Assuming the formula works at large angles like 90°.
- Confusing length with the amplitude .
KEY TAKEAWAYS
- Period depends only on and .
- Period is independent of mass.
- Period is independent of amplitude (small angle).
- Mechanical energy is conserved (PE to KE).
PRACTICE QUESTIONS
Q1 (QUANTITATIVE): A pendulum is taken from Earth to the Moon where is 1/6th as strong. How does the period change?
Show Answer & Explanation
Answer: Increases by times.
Explanation: . If becomes , becomes times longer.
