Explanation Calculation: Consider the given differential equation. d y d x = W T 1 Here, W is the vertical load. The per unit length of the roadbed is a constant ρ and the curve defining the cable is symmetric about x = 0 so only positive side of the bridge is to be conserved for the moment so, W = ρ x for 0 ≤ x ≤ L 2 The equation can be written as, d y d x = ρ x T 1 Separate the variable of the above equation. d y = ρ x T 1 d x Integrate on both sides of the equation. ∫ d y = ∫ ρ x T 1 d x y = ρ 2 T 1 x 2 + c Substitute a for y and 0 for x in the above equation. a = ρ 2 T 1 ( 0 ) 2 + c a = c Substitute a for c in above equation. y = ρ 2 T 1 x 2 + a The maximum height of ( a + h ) happens at the end of the bridge, x = L 2

Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th

11th Edition

ISBN: 9781305965737

Author: Dennis G. Zill

Publisher: Brooks Cole

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Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th

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