The Simple Pendulum

Explore oscillations & energy

  1. Set the string length, bob mass and release angle. Or drag the brass bob to set its starting angle.
  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. Use slow motion or pause to inspect the swing. Changing a setting resets the apparatus.

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.

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
Ready to explore.

Energy in motion

Energy bars share a scale. Total mechanical energy stays constant during each swing.

SMALL-ANGLE PERIOD
ACTUAL PERIOD
BOB SPEED
CURRENT ANGLE

T ≈ 2π√(L/g) for small angles

The actual period accounts for the larger release angle. Mass changes the energy, but not the period.

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.