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# Here is a different way to couple two oscillators. The two

ISBN: 9781891389221 90

## Solution for problem 11.12 Chapter 11

Classical Mechanics | 0th Edition

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Problem 11.12

Here is a different way to couple two oscillators. The two carts in Figure 11.16 have equal masses m (though different shapes). They are joined by identical but separate springs (force constant k) to separate walls. Cart 2 rides in cart 1, as shown, and cart 1 is filled with molasses, whose viscous drag supplies the coupling between the carts. (a) Assuming that the drag force has magnitude /3m v where v is the relative velocity of the two carts, write down the equations of motion of the two carts using as coordinates x1 and x2, the displacements of the carts from their equilibrium positions. Show that they can be written in matrix form as x + + (02:x = 0, where x is the 2 x 1 column made up of x1 and x2, coo = ,/k/m, and D is a certain 2 x 2 square matrix. (b) There is nothing to stop you from seeking a solution of the form x(t) = Re z(t), with z(t) = aert . Show that you do indeed get two solutions of this form with r = icoo or r = 13 + iwi where col = Jcoo )52. (Assume that the viscous force is weak, so that ,8 < coo.) (c) Describe the corresponding motions. Explain why one of these modes is damped but the other is not.

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Rosanna Cheng PH 106 02.17.17 and 02.23.17 Pages 560-580 Reading Journal Prediction The chapter will continue to discuss magnetism. Notes 20.1 Magnets and Magnetic Fields * Poles are the ends/faces of a magnet. The pole of a freely suspended magnet pointing toward north is north pole. The other is south pole. Like poles repel, unlike poles attract. Magnetic monopole doesn’t exist,...

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