9 In solving certain problems involving support beams in engineering, the fourth-order differential equation y"" = 2*y is encountered, which is sometimes written as y) = 2*y. a Show that y Aex + Be-Ax + C cos àx + D sin Ax is a solution of the DE. %3D b A beam rests on a support at a point O. At a horizontal distance x along the beam, the downwards deflection is y. Thus y (0) = 0, and we may also assume that y" (0) = 0. Find the value of C. c If the beam is also resting on a support at x = 10, then both y(10) = 0 and y" (10) = 0. From this it can be shown that 2 = 5. i Use these results to show that A = B = 0. ii Write down the solution of the beam IVP.
9 In solving certain problems involving support beams in engineering, the fourth-order differential equation y"" = 2*y is encountered, which is sometimes written as y) = 2*y. a Show that y Aex + Be-Ax + C cos àx + D sin Ax is a solution of the DE. %3D b A beam rests on a support at a point O. At a horizontal distance x along the beam, the downwards deflection is y. Thus y (0) = 0, and we may also assume that y" (0) = 0. Find the value of C. c If the beam is also resting on a support at x = 10, then both y(10) = 0 and y" (10) = 0. From this it can be shown that 2 = 5. i Use these results to show that A = B = 0. ii Write down the solution of the beam IVP.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:9 b C = 0
c ii y = D sin x
%3D
Transcribed Image Text:9 In solving certain problems involving support beams in engineering, the fourth-order differential
= 1ªy is encountered, which is sometimes written as y(4)
Ae1x + Be-x + C cos Ax + D sin Ax is a solution of the DE.
b A beam rests on a support at a point O. At a horizontal distance x along the beam, the downwards
equation y"
= ^*y.
a Show that y =
deflection is y. Thus y (0)
0, and we may also assume that y" (0)
= 0. Find the value of C.
C If the beam is also resting on a support at x =
10, then both y (10)
:0 and y" (10)
= 0. From this
it can be shown that 2
пл
10
i Use these results to show that A = B = 0.
ii Write down the solution of the beam IVP.
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