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Unformatted text preview: = 1 c c 2 y 2 = 1 + y 2 y = dy ddx = p c 2 y 2-1 Z dy p c 2 y 2-1 = Z dx To compute the integral on the left hand side, substitute cy = cosh . Z 1 c sinh d p cosh 2 -1 = x + A c = x + A y ( x ) = 1 c cosh = 1 c cosh c ( x + A ) The constant A can be determined using the condition y ( L ) = y (-L ) . 1 c cosh c (-L + A ) = 1 c cosh c ( L + A ) c (-L + A ) = c ( L + A ) If we take the positive sign, we get c = 0 , which is not physical. If we take the negative sign, we get A = 0 . Thus, y ( x ) = 1 c cosh cx. The constant c can be determined implicitly from calculating the total mass of the chain. 2...
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