Class Pendulum

java.lang.Object
org.episteme.natural.physics.classical.oscillations.Pendulum
public class Pendulum extends Object
Pendulum motion calculations.
Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Method Summary

    Modifier and Type
    Method
    Description
    static Real
    angularFrequency(Real lengthMeters)
    Angular frequency: ω = sqrt(g/L)
    static Real
    dampedAmplitude(Real initialAmplitude, Real dampingCoefficient, Real time)
    Damped amplitude: A(t) = A₀ * exp(-γt)
    static Real
    kineticEnergy(Real mass, Real lengthMeters, Real angularVelocity)
    Kinetic energy: KE = 0.5 * m * L² * ω²
    static Real
    largeAnglePeriod(Real lengthMeters, Real amplitudeRadians)
    Large angle period (elliptic integral approximation)
    static Real
    position(Real amplitude, Real omega, Real time, Real phase)
    Position at time t: θ(t) = θ₀ * cos(ωt + φ)
    static Real
    potentialEnergy(Real mass, Real lengthMeters, Real angleRadians)
    Potential energy: U = mgL(1 - cos(θ))
    static Real
    simplePendulumPeriod(Real lengthMeters)
    Simple pendulum period: T = 2Ï€ * sqrt(L/g)

    Methods inherited from class Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Method Details

    • simplePendulumPeriod

      public static Real simplePendulumPeriod(Real lengthMeters)
      Simple pendulum period: T = 2Ï€ * sqrt(L/g)

    • angularFrequency

      public static Real angularFrequency(Real lengthMeters)
      Angular frequency: ω = sqrt(g/L)

    • position

      public static Real position(Real amplitude, Real omega, Real time, Real phase)
      Position at time t: θ(t) = θ₀ * cos(ωt + φ)

    • dampedAmplitude

      public static Real dampedAmplitude(Real initialAmplitude, Real dampingCoefficient, Real time)
      Damped amplitude: A(t) = A₀ * exp(-γt)

    • largeAnglePeriod

      public static Real largeAnglePeriod(Real lengthMeters, Real amplitudeRadians)
      Large angle period (elliptic integral approximation)

    • potentialEnergy

      public static Real potentialEnergy(Real mass, Real lengthMeters, Real angleRadians)
      Potential energy: U = mgL(1 - cos(θ))

    • kineticEnergy

      public static Real kineticEnergy(Real mass, Real lengthMeters, Real angularVelocity)
      Kinetic energy: KE = 0.5 * m * L² * ω²