The Simple Pendulum

Explore oscillations & energy

  1. Choose a one-variable comparison and make a prediction. The dashed outline is the original pendulum; the brass bob is the changed setup. Release both together to compare their motion.
  2. Select Release bob. Watch the energy move between potential energy at the ends and kinetic energy at the bottom.
  3. Compare lengths while keeping the release angle fixed. Then change only the mass. What changes the period?
  4. Transport the apparatus to the Moon or Jupiter. Try zero gravity: a bob released from rest stays still because there is no restoring force.
  5. Pause and use Step +0.05 s to inspect energy transfer. A complete oscillation returns to the starting side, not just the opposite side. In Free exploration, use the sliders or drag the bob. Sliders also work with keyboard arrow keys. Changing a setting resets the motion and clears the comparison.

The reference and changed pendulums are drawn over each other to compare their timing. In the mass comparison their paths overlap because mass does not change the period. The ideal model has no air resistance or pivot friction, a massless rigid suspension and a point-mass bob. Length is measured from the pivot to the bob’s center. Potential energy is zero at the lowest position. At zero gravity the ideal suspension keeps its geometry; a real string would be slack.

What changes the swing?

Choose a comparison. Predict what will happen, then release both pendulums.

Start with a comparison, or adjust the apparatus to explore on your own.

The pendulum apparatus

EARTH LABORATORY
STEEL STAND / BRASS BOBIDEAL MECHANICS LAB
Laboratory pendulumA brass bob hangs from a clamp on a steel retort stand, next to a meter rule and an angle scale.Retort standZORNSCIENCE / OSCILLATIONS & ENERGY
READY TO RELEASE0.00 s

Energy in motion

Release the bob to follow the energy transfer.

Both bars use the same joule scale.

Ready to explore.
0 complete oscillationsRelease to start

A period is one full trip: starting side → opposite side → starting side. The clock shows simulation time.

SMALL-ANGLE PERIOD
MODEL PERIOD
BOB SPEED
CURRENT ANGLE

T ≈ 2π√(L/g) for small angles

The model period includes the release angle. The small-angle formula is a close approximation at 15° or less. Try a larger angle and compare.

About this model

Motion follows θ″ = −(g/L)sin θ using a fixed-step fourth-order Runge-Kutta integrator. The period uses the complete elliptic integral. At exactly zero amplitude there is no oscillation; the small-angle period is the limiting prediction. The stand is an ideal, anchored support in every environment.