Premium experiment • oscillation lab
PHYSICS • OSCILLATIONS
Pendulum
Measure a full oscillation, scrub phase, compare lengths, inspect energy exchange and tune the system to a target period while keeping the small-angle model explicit.
● LIVE OSCILLATIONEarth • small-angle model
Small-angle period0.00 s
Finite-angle estimate0.00 s
Reference period0.00 s
Target error0.00 s
Maximum speed0.00 m/s
Total energy0.00 J
Use the pendulum as a measurement instrument
Scrub through one complete cycle, inspect the phase portrait and watch potential energy exchange with kinetic energy. Change bob mass to verify that period stays unchanged while the energy scale changes.
Fast investigations
- Double the length and test the √L period relationship.
- Hold length fixed and switch Earth → Moon to isolate gravity.
- Change bob mass and confirm the predicted period does not move.
- Raise the starting angle toward 30° and compare the small-angle period with the finite-angle correction estimate.
LEARN WITH THE SIMULATION
Understand Pendulum by experimenting.
START HERE
A simple pendulum converts gravitational potential energy into kinetic energy and back again. For small angles, its period depends mainly on pendulum length and gravitational acceleration, not on bob mass.
BUILD THE IDEA
What you should understand first
- See how length changes oscillation period.
- Compare small-angle behavior with larger starting angles.
- Relate gravity to the natural timing of the pendulum.
TRY IT YOURSELF
What happens to the period when the pendulum length is quadrupled?
- Start with a short pendulum and record its period.
- Multiply the length by four while keeping gravity fixed.
- Compare the new period with the original.
Read the visual:
In the small-angle approximation, quadrupling length doubles the period because T is proportional to √L.
WHY IT WORKS 01
See how length changes oscillation period.
A simple pendulum converts gravitational potential energy into kinetic energy and back again. For small angles, its period depends mainly on pendulum length and gravitational acceleration, not on bob mass. Focus on the relationship between the controlled variable and the measured response rather than treating the visual change as the explanation.
WHY IT WORKS 02
Compare small-angle behavior with larger starting angles.
In the small-angle approximation, quadrupling length doubles the period because T is proportional to √L. Use an extreme or boundary setting after the baseline trial to check whether the same reasoning still holds.
DO NOT MIX THESE UP
Common misconception
Mass does not appear in the ideal period formula. The small-angle formula becomes less accurate at large amplitudes. The bob is fastest near the bottom, not at the turning points.
PRACTICE CHALLENGE
What happens to the period when the pendulum length is quadrupled?
- Start with a short pendulum and record its period.
- Multiply the length by four while keeping gravity fixed.
- Compare the new period with the original.
Reveal the reasoning
In the small-angle approximation, quadrupling length doubles the period because T is proportional to √L. Mass does not appear in the ideal period formula. The small-angle formula becomes less accurate at large amplitudes. The bob is fastest near the bottom, not at the turning points.
MODEL BOUNDARIES
What this simulation assumes
Every simulation simplifies reality or a mathematical system. These are the assumptions and limits to keep in mind while interpreting the results.
Model assumptions
- The bob is a point mass attached to a massless rigid-length string.
- The model uses the small-angle simple-harmonic approximation for the period and angular motion.
- Gravity is constant and damping is neglected.
Model limitations
- Accuracy decreases as the release angle becomes large; the simulator therefore limits the angle to the small-angle regime.
- Real pivots have friction, strings have mass and flexibility, and air resistance damps the motion.
CONNECT IT
Where this matters
- Clocks and timing devices
- Seismometers
- Gravity estimation
WORDS THAT MATTER
Key vocabulary
- Period
- Time for one complete oscillation.
- Amplitude
- Maximum displacement from equilibrium.
- Equilibrium
- The central resting position of the oscillator.
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