the even-indexed modes will not be excited because their generalized forces are also zero. For the odd-indexed modes the general solution to their equation of motion is

= Aj sin (wit) + Bi cos (w/t) + C, sin(&>f). (2.120)

It may be noted that the first two terms correspond to the homogeneous portion of the solution, whereas the third term represents the particular solution. In this example, the particular solution has the same form of time dependence as the generalized force.

To evaluate the constants A, and B, of the homogeneous solution, a procedure can be followed that is quite similar to the one used in Section 2.1.3 for solution of the homogeneous initial condition problem. The initial displacement of the present example can be written as og ckj / " \

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