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Unformatted text preview: Eq. (9) may be written as XI and X2: (11) X I = &W + i W J S , Xz = &W  i w J 1  E 2 . When k and M are real positive numbers, w is real, and the solution of Eq. (9) under the initial conditions (12) y(0) = yo , y(0) = yo when t = 0 . is EW t (13) y(t) = yoe cosw&2t Now, we can return to the solution of Eq. (3). A particular solution of Eq. (3) can be obtained by Laplace or Fourier transformation or other methods. By direct substitution, it can be verified that a particular solution satisfying the initial conditions y(t) = y(t) = 0 at t = 0 is: The general solution of Eq. (3) is the sum of the functions given in (13) and (14). From this solution we can examine the nature of the forced oscillation...
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This note was uploaded on 01/04/2012 for the course ENG 501 taught by Professor Thomson during the Fall '05 term at MIT.
 Fall '05
 Thomson
 Frequency, Natural Frequency

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