Home / Questions / Idealized spring-mass systems have numerous applications throughout engineering Figure sho...
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
Problem 6.109
A viscous fluid is contained between two infinitely long, vertical, concentric cylinders. The outer cylinder has a radius r_{o} and rotates with an angular velocity ω. The inner cylinder is fixed and has a radius r_{i}. Make use of the Navier–Stokes equations to obtain an exact solution for the velocity distribution in the gap. Assume that the flow in the gap is axisymmetric (neither velocity nor pressure are functions of angular position u within the gap) and hat there are no velocity components other than the tangential component. The only body force is the weight.
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