particle_on_spring_08

particle_on_spring_08 - Discontinuity in mechanics In...

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Discontinuity in mechanics In classical mechanics it was admitted the continuity of velocities, of ac- celerations and forces. The mechanical phenomena are continuous in time. There are cases when for very small time intervals there is a very large vari- ation of velocity, but the displacement in space of the particle is very small. If a sphere falls on a vertical spring, the sphere makes contact with the sphere. The spring compresses under the weight of the sphere. The com- pression phase ends when the velocity of the sphere is zero. Next phase is the restitution phase when the spring expanding and the sphere is moving upward. At the end of the restitution phase there is the separation of the sphere. The x -axis is selected downward. Assume that at moment t = 0 the sphere is in contact with the spring. At that moment the velocity of the sphere is v ( t = 0) = v 0 = v 0 ı . The equation of motion for the sphere in contact with the spring is m ¨ x = mg - k x, (1) where k is the spring constant ( k > 0). The contact force due to the elastic force is
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particle_on_spring_08 - Discontinuity in mechanics In...

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