Pendulum Energy

    Kinetic, Potential & Mechanical Energy

    KE = 0.00 J
    PE = 0.00 J
    θ = 45.0°

    Simulation

    Bob colour: blue = max PE (top) → orange = max KE (bottom)

    Energy Bars

    Energy vs Time

    KE   PE   Total E  

    Parameters

    Length L1.0 m
    0.3 m3 m
    Mass m1.0 kg
    0.1 kg5 kg
    Initial angle θ₀45°
    5°170°
    Damping b0.00
    01

    Calculated Values

    Initial total energyE₀ = 2.873 J
    Max heighth = 0.293 m
    Max speed (bottom)v = 2.397 m/s
    Period (small angle)T = 2.006 s
    Frequencyf = 0.498 Hz
    KE = ½mL²ω²
    PE = mgL(1 − cosθ)
    E = KE + PE = const

    Physics

    At the highest point all energy is potential (PE). At the lowest point all energy is kinetic (KE). Without damping their sum stays constant — conservation of mechanical energy.

    Adding damping b dissipates energy as heat. The total-energy line on the graph slopes downward and the bob's amplitude decreases each swing.

    The small-angle approximation gives T = 2π√(L/g). For large angles the true period is longer — try θ₀ > 90° to see the non-linear effect.