30: Simple Harmonic Oscillations of Suspended Solid Bodies

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Topics covered: The simple harmonic oscillations (SHO) of suspended solid bodies are related to their geometry. The torsional pendulum oscillates in the horizontal plane; the SHO does NOT depend on the small angle approximation.

Instructor/speaker: Prof. Walter Lewin

Date recorded: November 24, 1999

Video Index

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  • SHO of a Physical Pendulum
    The SHO equation of motion (small angle approximation) for a rigid body pendulum is derived from the torque equation about the point of suspension. The periods of oscillation are worked out for four different shapes (rod, hoop, disk and for a billiard ball hanging from a massless string).

  • SHO of a Liquid in a U-Tube
    The SHO equation of motion for a liquid sloshing in a U-shaped tube is derived by taking the time derivative of the conservation of mechanical energy. The angular frequency and period are calculated and compared to empirical data.

  • Torsional Pendulum
    The SHO equation of motion for a torsional pendulum is derived from the torque equation about the center of mass. The displacement angle is in the horizontal plane. The restoring torque is due to the twisted wire; no small angle approximations are required. The demo uses piano wire.

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  • English - US (SRT)