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1. 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).

2. 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.

3. 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.