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Experiment with nonlinear restoring forces, phase space velocities, and real-time kinetic vs. potential energy conservation in gravitational fields.
Applying Newton's second law for rotational systems (τ = Iα), the restoring torque is given by τ = −mgL sin(θ). For small angle amplitudes (θ ≤ 15°), we use the Taylor small-angle approximation sin(θ) ≈ θ:
Notice that the period $T$ is independent of bob mass ($m$) and depends only on string length ($L$) and local acceleration due to gravity ($g$).