241_pdfsam_math 54 differential equation solutions odd

241_pdfsam_math 54 differential equation solutions odd -...

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Exercises 4.8 and so y ( t )= ± 3 4 cos 8 t sin 8 t ² e 8 t = 5 4 e 8 t sin(8 t + φ ) , where tan φ =( 3 / 4) / ( 1) = 3 / 4andcos φ = 1 < 0. Thus, φ = π + arctan(3 / 4) 3 . 785 . The damping factor is (5 / 4) e 8 t , the quasiperiod is P =2 π/ 8= 4, and the quasifrequency is 1 /P =4 . 9. Substituting the values m , k = 40, and b =8 5 into equation (12) on page 213 in the text and using the initial conditions, we obtain the initial value problem 2 d 2 y dt 2 +8 5 dy dt +40 y =0 ,y (0) = 0 . 1(m) 0 (0) = 2 (m / sec) . The initial conditions are positive to reflect the fact that we have taken down to be positive in our coordinate system. The auxiliary equation for this system is 2 r
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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 Berkeley.

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