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Setups other learners found interesting in Simple Pendulum Simulation. Try one, then tweak it.

Simple Pendulum Simulation

A bob on a string swings back and forth about its lowest point. For small swings the motion is simple harmonic and the period depends only on the string length and gravity — not on the mass, and only weakly on the amplitude, the property Galileo called isochronism. Increase the initial angle to see the small-angle approximation break down.

Key formulas

  • T=2πLgT = 2\pi\sqrt{\dfrac{L}{g}}

    Period of a simple pendulum

    TT
    Periods
    LL
    Lengthm
    gg
    Gravitational accelerationm/s²
    Open the formula card
  • θ¨+gLsin⁡θ=0\ddot{\theta} + \dfrac{g}{L}\sin\theta = 0

    Pendulum equation of motion

    θ\theta
    Angle from the verticalrad
    θ¨\ddot{\theta}
    Angular accelerationrad/s²
    gg
    Gravitational accelerationm/s²
    LL
    Lengthm
    Open the formula card
  • v=2gL (1−cos⁡θ0)v = \sqrt{2 g L\,(1 - \cos\theta_0)}

    Pendulum speed at the bottom

    vv
    Speed at the bottomm/s
    gg
    Gravitational accelerationm/s²
    LL
    Lengthm
    θ0\theta_0
    Release angle°
    Open the formula card

What you can change

  • Length
  • Mass
  • Gravity
  • Damping
  • Initial angle

Key concepts

  • Restoring torque of gravity
  • Small-angle approximation, sin θ ≈ θ
  • Isochronism for small amplitudes
  • Energy conservation between the top and bottom of the swing