Using principles from physics it can be shown that when a cable is hung between two poles, it takes the shape of a curve y = f(x) that satisfies the differential equation d'y pg dy 2 1 + dx dx2 where p is the linear density of the cable, g is the accelera- tion due to gravity, T is the tension in the cable at its lowest point, and the coordinate system is chosen appro- priately. Verify that the function T cosh Pg pgx y = f(x) T is a solution of this differential equation.
Using principles from physics it can be shown that when a cable is hung between two poles, it takes the shape of a curve y = f(x) that satisfies the differential equation d'y pg dy 2 1 + dx dx2 where p is the linear density of the cable, g is the accelera- tion due to gravity, T is the tension in the cable at its lowest point, and the coordinate system is chosen appro- priately. Verify that the function T cosh Pg pgx y = f(x) T is a solution of this differential equation.
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Transcribed Image Text:Using principles from physics it can be shown that when a
cable is hung between two poles, it takes the shape of a
curve y = f(x) that satisfies the differential equation
d'y
pg
dy 2
1 +
dx
dx2
where p is the linear density of the cable, g is the accelera-
tion due to gravity, T is the tension in the cable at its
lowest point, and the coordinate system is chosen appro-
priately. Verify that the function
T
cosh
Pg
pgx
y = f(x)
T
is a solution of this differential equation.
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