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A lightweight cantilevered beam is supported at N points spaced 10 ft apart, and a weight of 500 lb is placed at the end of the beam, 10 ft from the first support, as in the figure. Let yk be the bending moment at the kth support. Then yl = 5000 ft-lb. Suppose the beam is rigidly attached at the Nth support and the bending moment there is zero. In between, the moments satisfy the three-moment equation Yk+2 + 4yk+1+ Yk = 0 _for k = 1,2,., N – 2 (15) /- -10'- -10' 10'– 500 (2) E, lb УN Bending moments on a cantilevered beam. Find the general solution of difference equation (15). Justify your answer.

A lightweight cantilevered beam is supported at N points spaced 10 ft apart, and a weight of 500 lb is placed at the end of the beam, 10 ft from the first support, as in the figure. Let yk be the bending moment at the kth support. Then yl = 5000 ft-lb. Suppose the beam is rigidly attached at the Nth support and the bending moment there is zero. In between, the moments satisfy the three-moment equation Yk+2 + 4yk+1+ Yk = 0 _for k = 1,2,., N – 2 (15) /- -10'- -10' 10'– 500 (2) E, lb УN Bending moments on a cantilevered beam. Find the general solution of difference equation (15). Justify your answer.

Advanced Engineering Mathematics
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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A lightweight cantilevered beam is supported at N points spaced 10 ft apart, and a weight of 500 lb is placed at the end of the beam, 10 ft from the first support, as in the figure. Let yk be the bending moment at the kth support. Then yl = 5000 ft-lb. Suppose the beam is rigidly attached at the Nth support and the bending moment there is zero. In between, the moments satisfy the three-moment equation Yk+2 + 4yk+1+ Yk = 0 _for k = 1,2,., N – 2 (15) /- -10'- -10' 10'– 500 (2) E, lb УN Bending moments on a cantilevered beam. Find the general solution of difference equation (15). Justify your answer.
Transcribed Image Text:A lightweight cantilevered beam is supported at N points spaced 10 ft apart, and a weight of 500 lb is placed at the end of the beam, 10 ft from the first support, as in the figure. Let yk be the bending moment at the kth support. Then yl = 5000 ft-lb. Suppose the beam is rigidly attached at the Nth support and the bending moment there is zero. In between, the moments satisfy the three-moment equation Yk+2 + 4yk+1+ Yk = 0 _for k = 1,2,., N – 2 (15) /- -10'- -10' 10'– 500 (2) E, lb УN Bending moments on a cantilevered beam. Find the general solution of difference equation (15). Justify your answer.
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