E

It should be noted from this solution that the modal contributions to the total displacement significantly decrease as the mode number (the index i) increases. This can be observed from the dependence of F, on i. This is characteristic of almost all structural dynamics response problems and thus permits a truncation of the infinite sum to a finite number of the lower-order modes. It also should be noted that the above solution indicates that the string will vibrate forever, with the string returning to its initial shape periodically. In real systems there are always dissipative phenomena that cause the motion to die out in time. This will be considered when we deal with aeroelastic flutter in Chapter 4.

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