Help with 2D mass-spring-damper system

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The discussion centers on understanding the dynamics of a 2D mass-spring-damper system, particularly the interaction between box2 and the ground. The confusion arises regarding the force applied to box2 and its effect on the spring k2, specifically why the force between box2 and the ground decreases. It is clarified that if the quantity (x2 - z) is positive, the lower spring is compressed rather than stretched. The conceptual difficulty is alleviated by expressing the spring force as +k2(z - x2), which is always positive in practice. This highlights the importance of proper interpretation of spring forces in the system's analysis.
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Homework Statement
box1 mass : m1
box2 mass : m2
box1 displacement : x1
box2 displacement : x2
ground displacement : z

k1(spring), b(damper) attached between box1, box2
k2(spring) attached between box2 and ground
force is applied to box1 and 2 as shown in image
Relevant Equations
mx'' = f - kx -bx' (F = ma)
아님.png


the image on the right shows the problem.

the blue ink is the equation someone else gave me,
and I don't understand why the force between box2 and ground goes down...
(the red is me)

the force f is applied to box2 so that it pushes box2 down,
so isn't the spring k2 supposed to push upward?
 
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If the quantity ##(x_2-z)## is positive, what can you say about the lower spring? Is it stretched or compressed?
 
TSny said:
If the quantity ##(x_2-z)## is positive, what can you say about the lower spring? Is it stretched or compressed?
In practice, of course, it never will be stretched, but the conceptual difficulty goes away if we write it as ##+k_2(z-x_2)## and note that this will always be positive.
 
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