Example 2-9-4 - Maple Help



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 $\left({x}_{1},{y}_{1}\right)$ and $\left({x}_{2},{y}_{2}\right)$ in a vertical $\mathrm{xy}$-plane, the equation describing the shape of the cable is of the form , with $c$ constrained by the equation .  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 $\left(0,1\right)$ and $\left(1,3/2\right)$, 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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