Example 2-9-4 - Maple Help

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Chapter 2: Differentiation

Section 2.9: The Hyperbolic Functions and Their Derivatives

Example 2.9.4

It can be shown that for a sufficiently idealized wire cable of length c, hanging between two supports at x1,y1 and x2,y2 in a vertical xy-plane, the equation describing the shape of the cable is of the form yx=k coshd+x/kλ, with c constrained by the equation c=k sinhd+x2/ksinhd+x1/k.  In this context, the curve is called a catenary, from the Latin catina (chain). If such a cable of length c=2 hangs between the points 0,1 and 1,3/2, find the equation of the resulting catenary, and draw its graph.


(In the typical North American pronunciation of catenary, the accent is on the first syllable; in the British, it is on the second: thus, cat'-ěn-ary and că-tēn'-ery, respectively.)

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