A flexible chain of length l is hung over a peg with one end of the chain slightly longer than the other. Assuming that the chain slides off with no friction, write and solve the differential equation of motion to show that y = y 0 cosh t 2 g / l , 0 < y < l / 2 , where 2 y is the difference in length of the two ends, and y = y 0 when t = 0 .
A flexible chain of length l is hung over a peg with one end of the chain slightly longer than the other. Assuming that the chain slides off with no friction, write and solve the differential equation of motion to show that y = y 0 cosh t 2 g / l , 0 < y < l / 2 , where 2 y is the difference in length of the two ends, and y = y 0 when t = 0 .
A flexible chain of length
l
is hung over a peg with one end of the chain slightly longer than the other. Assuming that the chain slides off with no friction, write and solve the differential equation of motion to show that
y
=
y
0
cosh
t
2
g
/
l
,
0
<
y
<
l
/
2
, where 2y is the difference in length of the two ends, and
y
=
y
0
when
t
=
0
.
Fundamentals of Differential Equations and Boundary Value Problems
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