Barton, Edwin H. (Edwin Henry), b. 1858 · London, Macmillan and Co., limited · leaf 315
ntral node. We have now to treat very briefly the sixth and onlyremaining case, namely, that with both ends supported.Referring to equations (20) and the conditions (8) we findthat at x = 0, y = 0 gives P = 0, and d2y/dx2 = 0 gives Q = 0.Again, at x = I, i.e. xf = m, we find y = 0 gives R — S = 0… … Fig. 57.—Approach of Nodes in a Bent Bar. R and S, the expression reduces to a single term, viz. thatinvolving sin x1. We may accordingly write x, . nirxy = K sm cos ~U 2 2 Kon - I1 IT—t + € (32), where K and e are arbitrary constants to be chosen tosatisfy the initial conditions. It is thus seen…
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