234_pdfsam_math 54 differential equation solutions odd

234_pdfsam_math 54 differential equation solutions odd -...

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Chapter 4 Thus (4.9) becomes ( θ 0 ) 2 2 cos θ =1 . In particular, at the initial moment, t =0 , [ θ 0 (0)] 2 2 cos[ θ (0)] = 1 . Since θ (0) = 0, we get [ θ 0 (0)] 2 2 cos 0 = 1 [ θ 0 (0)] 2 =4 θ 0 (0) = 2 or θ 0 (0) = 2 . 11. The “damping coefficient” in the Rayleigh equation is b =( y 0 ) 2 1. Thus, for low velocities y 0 ,w ehav e b< 0, and b> 0 for high velocities. Therefore, the low velocities are boosted, while high velocities are slowed, and so one should expect a limit cycle. 13.
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.

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