Part of JWAVE-01 — Simple Harmonic Motion

Angular SHM — Torsional Pendulum

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Angular SHM follows τ=Cθ\tau = -C\theta where CC is the torsional constant and θ\theta is the angular displacement. The equation of motion is Iθ¨=CθI\ddot{\theta} = -C\theta, giving ω=C/I\omega = \sqrt{C/I} and T=2πI/CT = 2\pi\sqrt{I/C}. For a physical (compound) pendulum of mass mm with COM at distance dd from pivot: T=2πI/(mgd)T = 2\pi\sqrt{I/(mgd)}, where II is the moment of inertia about the pivot. The equivalent simple pendulum length is leq=I/(md)l_{\text{eq}} = I/(md).

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