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If the force of Problem is concentrated at x = l/3, determine which modes will be absent in the solution

Problem

A siender rod of length I, free at x = 0 and fixed at x = I, is struck longitudinally by a time-varying force concentrated at the end x = 0.

Show that all modes are equally excited (i.e., that the mode-participation factor is independent of the mode number), the compIete solution being

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