Question: When a flexible cable of uniform density is suspended between two fixed points and hangs of its own weight, the shape y = f(x) of

When a flexible cable of uniform density is suspended between two fixed points and hangs of its own weight, the shape y = f(x) of the cable must satisfy a differential equation of the form where is a positive constant. Consider the cable shown in the figure.
(a) Let z = dy/dx in the differential equation. Solve the resulting first-order differential equation (in ), and then integrate to find y.
(b) Determine the length of the cable.

d'y dx dy dx -b, h) (b, h) (0, a) -b

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a dy dr Z Setting z Formula 25 gives lnz 1z kxc 1z Cekz 2 k1 C a 2k y 2 dy 1 2k then y 1 20 C 2k z k ... View full answer

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