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Idealized spring-mass systems have numerous applications throughout engineering. Figure 1
shows an arrangement of four springs in series being depressed with a force of 2000 N. At
equilibrium, force-balance equations can be developed defining the interrelationships between
the springs,
??2 (??2 - ??1) = ??1??1
??3 (??3 - ??2 ) = ??2 (??2 - ??1 )
??4 (??4 - ??3 ) = ??3 (??3 - ??2 )
?? = ??4 (??4 - ??3 )
where the ??'?? are spring constants. If ??1 through ??4 are 150, 50, 75, and 225 N/m, respectively,
compute the ??'?? using:
(a) Cramer’s rule
(b) Gauss Elimination
(c) Gauss Jordan
(d) LU decomposition
(e) Gauss Seidel
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