- Idealized spring-mass systems have numerous of applications in engineering Consider an arrangement of four springs with spring constants k being pressed with a force of 2000 N. At equilibrium, force-balance equations can be developed defining interrelationships between the springs as follows: k, (x, -x,) =k,x, k,(x, - x,) = k,(x, -x,) k (x, -x,) = k,(x, – x,) F=k,(x. - x,) a) Obtain [A] {x}={b} system where [A] cotains k values, {x} contains unknown x values and {b} contains F. b) Substituting k=150, k=50, k=75 and k=225 kg/s and F value into the system, obtain inverse of [A] by Gauss-Jordan Method. c) What are the x values?
- Idealized spring-mass systems have numerous of applications in engineering Consider an arrangement of four springs with spring constants k being pressed with a force of 2000 N. At equilibrium, force-balance equations can be developed defining interrelationships between the springs as follows: k, (x, -x,) =k,x, k,(x, - x,) = k,(x, -x,) k (x, -x,) = k,(x, – x,) F=k,(x. - x,) a) Obtain [A] {x}={b} system where [A] cotains k values, {x} contains unknown x values and {b} contains F. b) Substituting k=150, k=50, k=75 and k=225 kg/s and F value into the system, obtain inverse of [A] by Gauss-Jordan Method. c) What are the x values?
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- Idealized spring-mass systems have numerous of applications in engineering. Consider an
arrangement of four springs with spring constants k being pressed with a force of 2000 N. At
equilibrium, force-balance equations can be developed defining interrelationships between the
springs as follows:
k, (x, - x,) = k,x,
k, (x, - x,) = k, (x, -x,)
k,(x, - x,) = k, (x, - x,)
F=k,(x,- x,)
a) Obtain [A] {x}={b} system where [A] contains k values,
{x} contains unknown x values and {b} contains F.
b) Substituting k=150, k=50, k=75 and k=225 kg/s
and F value into the system, obtain inverse of [A] by
Gauss-Jordan Method.
c) What are the x values?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26e6ea22-d0a6-4023-bb04-4d6f588df127%2F699b2d27-98bd-4556-aa1a-5093342fad05%2Fk076wl_processed.png&w=3840&q=75)
Transcribed Image Text:3- Idealized spring-mass systems have numerous of applications in engineering. Consider an
arrangement of four springs with spring constants k being pressed with a force of 2000 N. At
equilibrium, force-balance equations can be developed defining interrelationships between the
springs as follows:
k, (x, - x,) = k,x,
k, (x, - x,) = k, (x, -x,)
k,(x, - x,) = k, (x, - x,)
F=k,(x,- x,)
a) Obtain [A] {x}={b} system where [A] contains k values,
{x} contains unknown x values and {b} contains F.
b) Substituting k=150, k=50, k=75 and k=225 kg/s
and F value into the system, obtain inverse of [A] by
Gauss-Jordan Method.
c) What are the x values?
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