- 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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Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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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