Suspension Bridge In (16) of Section 1.3 we saw that

a mathematical model for the shape of a flexible cable

strung between two vertical supports is

, (10)

where W denotes the portion of the total vertical load

between the points P1 and P2 shown in Figure 1.3.7. The

DE (10) is separable under the following conditions that

describe a suspension bridge.

Let us assume that the x- and y-axes are as shown in

Figure 2.2.5—that is, the x-axis runs along the horizontal

roadbed, and the y-axis passes through (0, a), which

is the lowest point on one cable over the span of the

bridge, coinciding with the interval [L
2, L
2]. In the

case of a suspension bridge, the usual assumption is that

the vertical load in (10) is only a uniform roadbed distributed

along the horizontal axis. In other words, it is

assumed that the weight of all cables is negligible in

comparison to the weight of the roadbed and that the

weight per unit length of the roadbed (say, pounds per

horizontal foot) is a constant . Use this information to

set up and solve an appropriate initial-value problem

from which the shape (a curve with equation y 
(x))

of each of the two cables in a suspension bridge is

determined. Express your solution of the IVP in terms

of the sag h and span L. See Figure 2.2.5.