θ = +25.0°v = 0.00 m/sh = 0.094 m
💡 Drag the bob to set initial release angle
t = 0.00 s
Mechanical Energy Conservation
E_total = 0.92 JGravitational (U = mgh)0.92 J
Kinetic Energy (K)0.00 J
Total Energy (E)0.92 J
Angular Displacement vs. Time (θ–t)[°]
Gravitational Field
g = 9.81 m/s²
Pendulum Length (L)1.00 m
Initial Release Angle (θ₀)25°
Small-angle (≤ 15°)Large nonlinear (≥ 45°)
Bob Mass (m)1.0 kg
Period Analysis & Nonlinearity
Small-Angle Approx (T₀)2π√(L/g)
2.006 sTrue Nonlinear Period (T)Exact Integration
2.030 sDiscrepancy+1.20%
Pendulum Governing Formulas
Equation of Motion:
d²θ/dt² = -(g/L) · sin(θ)
Total Mechanical Energy:
E = mgL(1 - cos θ) + ½m(Lω)²
Physics Conceptual Challenge
Question 1 of 4If you quadruple the length of a simple pendulum (L → 4L), what happens to its period of oscillation (T)?
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