P01 - Group Project MAP 2302 In class we have looked at...

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Group Project MAP 2302 In class we have looked at Newton’s Law F = ma on different occasions as a differential equation. You might reference those explorations as you work through this exercise set. Here we will look at its application to a simple mass-spring system. Throughout, x will refer to the position of the mass attached to the spring as it moves in a straight line, where x = 0 is the equillibrium position of the spring. By Hooke’s law, the force of the spring acting on the mass is proportional to x and acts in the direction opposite of the sign of x , that is, F = - kx for some k > 0 . 1. Suppose the spring shown in the figure at right, is stretched a distance A from its equilibrium position. Here, we assume there are no forces other than the spring. (a) Write a first-order differential equation in v and x for the motion using Newton’s Law. By what method is this equation easily solved? are the solutions unique? (b) Solve the initial value problem for this spring equation corresponding to the condition
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This note was uploaded on 12/15/2011 for the course MAP 2302 taught by Professor Tuncer during the Spring '08 term at University of Florida.

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P01 - Group Project MAP 2302 In class we have looked at...

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