9. Two swings are hanging from a 3 meter rectangular wood beam embedded at both ends. Swing 1 is attached at x = 1 m and swing 2 is attached at x = 2m. The person on swing 1 applies a point force of A Newton and the person on swing 2 applies a point force of B newton downwards. The differential equation is y'''' = A 8( x − 1) + — B 8(x - 2) with the four boundary conditions y(0) = 0 and y'(0) = 0 y''(0) = P and y'''(0) = Q. Determine the deflection of the beam as a function of x in terms of A, B, E, I, P and Q using the Laplace transform. Express your solution as a piecewise function. 9.1 Applying the Laplace transform, will result in the expression for L{y} term 1 term 2 term 3 term 4 P 1 L{y} + + 920 S e⁹185 (s**) 917 EI (s**) + BI (5810) EI 919 9.2 Term 1 can be expressed as L{P 9211**} 9.3 Term 4 can be expressed as L L{B 922 (t − 923) 924 H (t – ** - **)} =-
9. Two swings are hanging from a 3 meter rectangular wood beam embedded at both ends. Swing 1 is attached at x = 1 m and swing 2 is attached at x = 2m. The person on swing 1 applies a point force of A Newton and the person on swing 2 applies a point force of B newton downwards. The differential equation is y'''' = A 8( x − 1) + — B 8(x - 2) with the four boundary conditions y(0) = 0 and y'(0) = 0 y''(0) = P and y'''(0) = Q. Determine the deflection of the beam as a function of x in terms of A, B, E, I, P and Q using the Laplace transform. Express your solution as a piecewise function. 9.1 Applying the Laplace transform, will result in the expression for L{y} term 1 term 2 term 3 term 4 P 1 L{y} + + 920 S e⁹185 (s**) 917 EI (s**) + BI (5810) EI 919 9.2 Term 1 can be expressed as L{P 9211**} 9.3 Term 4 can be expressed as L L{B 922 (t − 923) 924 H (t – ** - **)} =-
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Assist please
Transcribed Image Text:9. Two swings are hanging from a 3 meter rectangular wood beam embedded at both ends. Swing 1 is
attached at x = 1 m and swing 2 is attached at x = 2m. The person on swing 1 applies a point
force of A Newton and the person on swing 2 applies a point force of B newton downwards.
The differential equation is y =
¡A 8(x − 1) + B8(x − 2) with the four boundary
AS
-
conditions y(0) = 0 and y'(0) = 0 y''(0) = P and y''(0) = Q. Determine the deflection of the
beam as a function of x in terms of A, B, E, I, P and Q using the Laplace transform. Express your
solution as a piecewise function.
9.1 Applying the Laplace transform, will result in the expression for L{y}
term 1 term 2
term 3
term 4
P
L{y}:
+
+
920 S
1
(S**)
-e⁹185
(s**) (5917)
+ BI (1919)
9.2 Term 1 can be expressed as_L{P_921t**}
9.3 Term 4 can be expressed as L
L{B 922 (1-923) 924 (t
-**)}
9.4 In expressing the solution y as a piecewise function, the part corresponding to the interval
1 < x < 2 has non zero terms:
y(x) =P**+Q**
· 925 = 0
y(x) =P**+Q**+
**
... 925 = 1
y(x) =P**+Q**+
**+
... 925 = 2
=
EI
EI
EI
**
e
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
