# Help with 2D mass-spring-damper system

• newbeee

#### newbeee

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)

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?

If the quantity ##(x_2-z)## is positive, what can you say about the lower spring? Is it stretched or compressed?

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.

newbeee