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rod_spring_08

# rod_spring_08 - Impact of a compound pendulum with a spring...

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Unformatted text preview: Impact of a compound pendulum with a spring Figure 1 depicts a uniform rod of mass m and length L and a spring with elastic constant k . The rod is connected to the ground by a pin joint and is free to rotate in a vertical plane and the end point of the rod makes contact with the spring. The spring compresses under the weight of the rod. The compression phase ends when the velocity of the end point of the rod is zero. Next phase is the restitution phase, when the spring expands and the rod is moving upward. At the end of the restitution phase there is the separation of the end point of the rod from the spring. The plane of motion will be designated the xy plane. The y-axis is ver- tical, with the positive sense directed vertically upward. The x-axis is hori- zontal and is contained in the plane of motion. The z-axis is also horizontal and is perpendicular to the plane of motion. These axes define an inertial reference frame. The unit vectors for the inertial reference frame are ı , , and k . The mass center of the rod is at the point C . As the rod is uniform, its mass center is coincident with its geometric center. The mass center, C , is at a distance L/ 2 from the pivot point O fixed to the ground, and the position vector is r OC = r C = x C ı + y C , where x C and y C are the coordinates of C x C = L 2 cos θ, y C = L 2 sin θ....
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rod_spring_08 - Impact of a compound pendulum with a spring...

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