214_pdfsam_math 54 differential equation solutions odd

214_pdfsam_math 54 differential equation solutions odd -...

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Chapter 4 0 0.5 1 1.5 0.2 0.4 0.6 0.8 1 | A ( V ) | 0 . 73 V Figure 4–A : The graph of the function | A ( V ) | . C 3 sin π 2 V + C 4 cos π 2 V = V V 2 1 cos π V + V V 2 1 = 2 V V 2 1 cos 2 π 2 V . The solution of this system is C 3 =0 ,C 4 = 2 V V 2 1 cos π 2 V . So, y 2 ( t )= 2 V V 2 1 cos π 2 V sin t. (b) The graph of the function | A ( V ) | = ± ± ± ± 2 V V 2 1 cos π 2 V ± ± ± ± is given in Figure 4-A. From this graph, we ±nd that the most violent shaking of the vehicle (the maximum of | A ( V ) | ) happens when the speed V 0 . 73 . 47.
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