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Figure 2.8 Concentrated force acting on string.

Figure 2.8 Concentrated force acting on string.

It may be recalled that the Dirac delta function can be thought of as the limiting case of a rectangular shape with area held constant and equal to unity as its width goes to zero. Thus, it may be defined by its integral property; for example, for a < x0 < b f

As a consequence, the above integral expression for the generalized force can be applied to the concentrated load so that

Example 3: Calculation of Forced Response

An example of a dynamically loaded string will be considered to illustrate the generalized force computation and subsequent solution for the string displacement. The specific example will be a uniformly distributed load of simple harmonic amplitude (in time) shown in Fig. 2.9 with

The initial string displacement and velocity will be taken as zero. Computation of the generalized force is simply

Considering the even- and odd-indexed modes separately one has

With the above, the generalized equations of motion become

2 Ft

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