Mechanics
Pendulum
Watch the bob speed up at the bottom and pause at the top of each swing.
Explore simple pendulum motion with an adjustable length and release angle. Measure period, frequency, and energy exchange between kinetic and gravitational potential energy in real time.
Simple harmonic motion
A pendulum swings back and forth because gravity provides a restoring force toward equilibrium. For small angles, the motion is approximately simple harmonic.
When the bob is displaced, gravity's component along the arc pulls it back toward the lowest point. That restoring force makes the bob oscillate — speeding up at the bottom, slowing at the turning points, repeating in a regular cycle.
- T ≈ 2π√(L/g) (small angles)
- Restoring force ∝ displacement (small θ)
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
If you double a pendulum's length, what happens to its period? Does making the bob heavier change the period at all?
Predictions to weigh
- 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.
Variable roles
What you set:
- Mass (kg)
- Rope Length (m)
- Release Angle (°)
What you measure:
- Period (s)
- Max Speed (m/s)
How the investigation runs
- 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.
Governing equation
Pendulum Period (Small-Angle) — T = 2π·√(L / g)
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 — PE = m·g·h
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.
What the printable worksheet asks students to work out
- 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.
Where this shows up beyond the lab
- 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?
- AP Physics 1 — Unit 7: Oscillations
- AP Physics C: Mechanics — Unit 7: Oscillations
- IB Physics — A.1 Kinematics
- IB Physics — C.1 Simple harmonic motion
- General High School Physics — Waves & sound
- NGSS High School Physics — Energy accounting in systems
- Middle School Physical Science — Stored (potential) energy
- Welcome to the pendulum
- Select the bob
- Press Play
- Back and forth
- Open the data
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.