Chapter 12, Problem 33P

Mechanical/Aerospace Engineering

Idealized spring-mass systems have numerous applications throughout engineering. Figure P12.33 shows an arrangement of four springs in series being depressed with a force of 2000 kg. At equilibrium, force-balance equations can be developed defining the inter relationships between the springs,

FIGURE P12.33

$k_2\left(x_2-x_1\right)=k_1{x}_1$

$k_3\left(x_3-x_2\right)=k_2\left(x_2-x_1\right)$

$k_4\left(x_4-x_3\right)=k_3\left(x_3-x_2\right)$

$F=k_4\left(x_4-x_3\right)$

where the k's are spring constants. If $k_1$ through $k_4$ are 150, 50, 75, and 225 N/m, respectively, compute the x' s.