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3. If only one person is on the swing in the image below, it is comparable to a point load of F = 500 N placed at x = 0.5 m on a wooden branch embedded at one end (cantilever). The length of the branch is 1.5 m. It is given that1 = 1 x 10- m" and E = 2 x 10° Nm-. The boundary conditions are y(0) = 0, y'(0) = 0, y"(0) = M and y'"(0) = -2M. Use your notes to model the fourth order differential equation suited to this application. Present you differential equation with y" subject of the equation. Use the Laplace transform to solve this equation in terms of M. Use your solution to determine the value of M at x = 0.5 m where this branch will break (deflection more than thresh y 2 -). Do not use Matlab as its solution will not be identifiable in the solution entry. 240

3. If only one person is on the swing in the image below, it is comparable to a point load of F = 500 N placed at x = 0.5 m on a wooden branch embedded at one end (cantilever). The length of the branch is 1.5 m. It is given that1 = 1 x 10- m" and E = 2 x 10° Nm-. The boundary conditions are y(0) = 0, y'(0) = 0, y"(0) = M and y'"(0) = -2M. Use your notes to model the fourth order differential equation suited to this application. Present you differential equation with y" subject of the equation. Use the Laplace transform to solve this equation in terms of M. Use your solution to determine the value of M at x = 0.5 m where this branch will break (deflection more than thresh y 2 -). Do not use Matlab as its solution will not be identifiable in the solution entry. 240

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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3. If only one person is on the swing in the image below, it is comparable to a point load of F = 500 N placed at x = 0.5 m on a wooden branch embedded at one end (cantilever). The length of the branch is 1.5 m. It is given that / = 1 x 10-6 m* and E = 2 × 10° Nm-2. The boundary conditions are y(0) = 0, y'(0) = 0, y'"(0) = M and y'"(0) = -2M. Use your notes to model the fourth order differential equation suited to this application. Present you differential equation with y' subject of the equation. Use the Laplace transform to solve this equation in terms of M. Use your solution to determine the value of M at x = 0.5 m where this branch will break (deflection more than thresh y 2). Do not use Matlab as its solution will not be identifiable in the solution entry. 240 You must indicate in your solution: 1. The simplified differential equation in terms of the deflection y you will be solving 2. The simplified Laplace transform of this equation where you have made L{y} subject of the equation 3. The partial fractions process if required 4. The completing the square process if required 5. Express the solution y as a piecewise function and determine the value of M at breakpoint when x = 0.5 m
Transcribed Image Text:3. If only one person is on the swing in the image below, it is comparable to a point load of F = 500 N placed at x = 0.5 m on a wooden branch embedded at one end (cantilever). The length of the branch is 1.5 m. It is given that / = 1 x 10-6 m* and E = 2 × 10° Nm-2. The boundary conditions are y(0) = 0, y'(0) = 0, y'"(0) = M and y'"(0) = -2M. Use your notes to model the fourth order differential equation suited to this application. Present you differential equation with y' subject of the equation. Use the Laplace transform to solve this equation in terms of M. Use your solution to determine the value of M at x = 0.5 m where this branch will break (deflection more than thresh y 2). Do not use Matlab as its solution will not be identifiable in the solution entry. 240 You must indicate in your solution: 1. The simplified differential equation in terms of the deflection y you will be solving 2. The simplified Laplace transform of this equation where you have made L{y} subject of the equation 3. The partial fractions process if required 4. The completing the square process if required 5. Express the solution y as a piecewise function and determine the value of M at breakpoint when x = 0.5 m
4. If a lion lies stretched out over the entire length of the branch in question 3, exerting a constant force of F = 500N/m over the entire length of the 1.5 m branch. It is given that I = 1x 10-6 m and E = 2x 10° Nm2. The boundary conditions are y(0) = 0, y'(0) = 0, y"(0) = M and y''(0) = -2M. Use your notes to model the fourth order differential equation suited to this application. Present you differential equation with y'' subject of the equation. Use direct integration and solve this equation in terms of M. Determine the deflection (in terms of M) at x = 1.5 m. Do not use Matlab as its solution will not be identifiable in the solution entry. You must indicate in your solution: 1. The simplified differential equation in terms of the deflection y you will be solving 2. All the steps associated with direct integration 3. The substitution process required for determining constants of integration 4. Express the solution y and determine the deflection at x = 1.5 m
Transcribed Image Text:4. If a lion lies stretched out over the entire length of the branch in question 3, exerting a constant force of F = 500N/m over the entire length of the 1.5 m branch. It is given that I = 1x 10-6 m and E = 2x 10° Nm2. The boundary conditions are y(0) = 0, y'(0) = 0, y"(0) = M and y''(0) = -2M. Use your notes to model the fourth order differential equation suited to this application. Present you differential equation with y'' subject of the equation. Use direct integration and solve this equation in terms of M. Determine the deflection (in terms of M) at x = 1.5 m. Do not use Matlab as its solution will not be identifiable in the solution entry. You must indicate in your solution: 1. The simplified differential equation in terms of the deflection y you will be solving 2. All the steps associated with direct integration 3. The substitution process required for determining constants of integration 4. Express the solution y and determine the deflection at x = 1.5 m
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