Harmonic Oscillations
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Determine the equation of motion as a function of time and the period of oscillations to a simple pendulum in the small oscillation approximation.
Solution using Newton's Second Law

Solution using Angular Momentum

Solution using Energy

Determine the equation of motion as a function of time and the period of oscillations for a physical pendulum, it consists of a body of any shape and mass m where the position of the center of mass is known in the small oscillation approximation.

Determine the equation of motion as a function of time and the period of oscillations for a physical pendulum in the small oscillation approximation. It consists of a thin disk of mass m and radius a, the disk oscillates around an axis placed on the edge of the disk.

A sledgehammer consists of a handle of mass 0.6 kg and 70 cm in length and a head of 3 kg and 6 cm in width. Calculate the moment of inertia and period of oscillations of this tool as it swings around a point at the upper end of the handle. Assume g = 9.8 m/s2 for the acceleration due to gravity.
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