Simple Pendulum
1 · Predict
If you double a pendulum's length, what happens to its period? Does making the bob heavier change the period at all?
- A longer pendulum has a longer period (swings back and forth more slowly); mass has no effect.
- A longer pendulum has a shorter period (swings back and forth more quickly).
- A heavier bob swings more slowly, regardless of the rope length.
2 · Set Up
- Open the Pendulum preset in the mechanics sandbox.
- Confirm the speed probe on the bob is live in the Math panel — you'll read its peak value at the bottom of each swing.
- For each row, set the bob's mass, the rope length, and the release angle from vertical, then release the bob and let it swing.
3 · Collect Data
| Mass (kg) | Rope Length (m) | Release Angle (°) | Period (s) | Max Speed (m/s) |
|---|---|---|---|---|
| 1 | 1 | 15 | ||
| 1 | 1.5 | 20 | ||
| 1 | 2 | 10 |
Graph period (s) vs. rope length (m) for your three rows. Is the relationship a straight line?
4 · Analyze
- For one row, compute the bob's max speed at the bottom of the swing using energy conservation (½mv² = mgh, with h = L(1 − cos θ₀)) and compare it to your live speed-probe reading. Do they agree?
- Look at the period column across all three rows. Does it depend on the bob's mass? Use the formula to explain why or why not.
5 · Extend
- The period formula T = 2π√(L/g) assumes small release angles. Predict what happens to the real period as the release angle grows past 30°— would the sandbox's measured period still match the formula?
- At the bottom of the swing, the pendulum is moving fastest. Where did its initial gravitational potential energy go, and why does the total stay (almost) constant over many swings?
The Physics Behind This Experiment
Pendulum Period (Small-Angle)
For small release angles, a simple pendulum's period depends only on its length and gravity — not on the mass of the bob or how far it's released.
Gravitational Potential Energy
The height the bob drops from its release point to the bottom of the swing, h = L(1 − cos θ₀), sets how much potential energy converts to kinetic energy — and so how fast the bob is moving at the bottom.