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[Computer] In general, the analysis of coupled oscillators

ISBN: 9781891389221 90

Solution for problem 11.10 Chapter 11

Classical Mechanics | 0th Edition

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Problem 11.10

[Computer] In general, the analysis of coupled oscillators with dissipative forces is much more complicated than the conservative case considered in this chapter. However, there are a few cases where the same methods still work, as the following problem illustrates: (a) Write down the equations of motion corresponding to (11.2) for the equal-mass carts of Section 11.2 with three identical springs, but with each cart subject to a linear resistive force by (same coefficient b for both carts). (b) Show that if you change variables to the normal coordinates 1 = 4 (xi + x2) and 2 = 4.(x1 x2), the equations of motion fort and 2 are uncoupled. (c) Write down the general solutions for the normal coordinates and hence for x1 and x2. (Assume that b is small, so that the oscillations are underdamped.) (d) Find x1(t) and x2(t) for the initial conditions x1(0) = A and x2(0) = v1(0) = v2(0) = 0, and plot them for 0 < t < 107r using the values A = k = m = 1, and b = 0.1.

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Chapter 1 ­ Introduction  Physics o The study of nature  The Domains of Physics o Microscopic Domain  The domain of atoms, molecules, electrons, protons, pion and mesons, etc.  Extreme small in mass  Uncertainty of physical properties  Unpredictable behavior o Macroscopic...

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