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242_pdfsam_math 54 differential equation solutions odd

# 242_pdfsam_math 54 differential equation solutions odd -...

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Chapter 4 The maximum displacement of the mass is found by determining the first time the velocity of the mass becomes zero. Therefore, we have y ( t ) = 0 = 2 + 0 . 2 5 e 2 5 t 2 5 0 . 1 + 2 + 0 . 2 5 t e 2 5 t , which gives t = 2 2 5(2 + 0 . 2 5) = 1 5(2 + 0 . 2 5) . Thus the maximum displacement is y 1 5(2 + 0 . 2 5) = 0 . 1 + 2 + 0 . 2 5 1 5(2 + 0 . 2 5) e 2 5 / [ 5(2+0 . 2 5)] 0 . 242 (m) . 11. The equation of the motion of this mass-spring system is y + 0 . 2 y + 100 y = 0 , y (0) = 0 , y (0) = 1 . Clearly, this is an underdamped motion because b 2 4 mk = (0 . 2) 2 4(1)(100) = 399 . 96 < 0 . So, we use use equation (16) on page 213 in the text for a general solution. With α = b 2 m
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