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Unformatted text preview: 3 cosh x + B 3 Or X = A 4 sinh x + B 4 Which form to use, depends on the boundary conditions. Recall that the hypebolic sine vanishes ONLY at x = 0 and the hyperbolic cosine is always positive. If we use the following form of the general solution X = A 4 sinh x + B 4 then the derivative X wil be X = A 4 cosh x + B 4 The Frst boundary condition X (0) = 0 yields B 4 = 0 and clearly to satisfy the second boundary condition A 4 cosh L = 0 we must have A 4 = 0 (recall cosh x is never zero thus the coecient A 4 must vanish). 23...
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- Fall '08