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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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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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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