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## Point Force Applied to the System

A unit force localized at a point is a unit force distributed over an -interval surrounding the given point. The density of this distributed force is inversely proportional to . More precisely, one defines

the finite approximation to the Dirac distribution, whose integral, the total force,

is unity. Let us apply such a force density,

to a string with constant horizontal tension . The response of this string is governed by the Poisson equation (4.13), namely

Note that the sum of all the vertical forces is necessarily zero. This equilibrium condition is expressed by the statement that (see Fig. 4.2)

or by

which is known as the jump condition. Here we are using the notation with neglegibly small. The other condition that the response must satisfy is that it be continuous at , i.e.

This continuity condition, the jump condition, together with the boundary conditions lead to a unique response, the Green's function of the string.(Why?)

Next: Properties and Utility of Up: Pictorial Definition of a Previous: The Simple String and   Contents   Index
Ulrich Gerlach 2010-12-09