# Applications of Harmonic Motion

### Problems

Problem : A disk of mass 2 kg and radius .5 m is hung from a wire, then rotated a small angle such that it engages in torsional oscillation. The period of oscillation is measured at 2 seconds. Given that the moment of inertia of a disk is given by I = , find the torsional constant, κ , of the wire.

Problem : The disk from problem 1 is replaced with an object of unknown mass and shape, and rotated such that it engages in torsional oscillation. The period of oscillation is observed to be 4 seconds. Find the moment of inertia of the object.

Problem : A pendulum of length L is displaced an angle θ , and is observed to have a period of 4 seconds. The string is then cut in half, and displaced to the same angle θ . How does this effect the period of oscillation?

Problem : A pendulum is commonly used to calculate the acceleration due to gravity at various points around the earth. Often areas with low acceleration indicate a cavity in the earth in the area, many times filled with petroleum. An oil prospector uses a pendulum of length 1 meter, and observes it to oscillate with a period of 2 seconds. What is the acceleration due to gravity at this point?

Problem : What is the angular velocity of a particle moving in uniform circular motion that has the same period as a mass of 2 kg on a spring with constant 8 N/m?

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