Idealized spring-mass systems have numerous applications throughout engineering…. 1 answer below »

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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