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.