Idealized spring-mass systems have numerous applications throughout engineering. Figure shows an arrangement of four springs in series

Question:

Idealized spring-mass systems have numerous applications throughout engineering. Figure shows an arrangement of four springs in series being depressed with a force of 1500 kg. At equilibrium, force-balance equations can be developed defining the interrelationships between the springs,

k₂(x₂ ? x₁) = k₁x₁

k₃(x₃ ? x₂) = k₂(x₂ ? x₁)

k₄(x₄ ? x₃) = k₃(x₃ ? x₂)

?F = k₄(x₄ ? x₃)

Where the k?s are spring constants. If k₁ through k₄ are 100, 50, 80, and 200 N/m, respectively, computed the x?s.