(a) Obtain the Maclaurin series expansions of sinh x and cosh x.

(b) A telegraph wire is stretched between two poles at the same height and a distance 2l apart. The sag at the midpoint is h. If the axes are taken as shown in Figure 9.27, it can be shown that the equation of the curve followed by the wire is

where c is an undetermined constant.
(i) Show that the length 2s of the wire is given by

(ii) If the wire is taut, so that h/c is small, it can be shown that l/c is also small. Ignoring powers of l/c higher than the second, show that

Hence show that the length of the wire is approximately

Figure 9.27

Transcribed Image Text:

X y = ccosh-