# Decomposition of Spring

Can a spring respectively its stiffness in a 2D-system be decomposed into its x- and y- components (stiffnesses)?

Assuming a spring located in an 2D coordinate system with positions p(x,y), length l and angle alpha, describing the orientation of the spring inside the system. Can the spring be represented by its xx, xy, yx and yy components?

Imagine an object which interacts with the spring not along its main direction, but along the global x-axis. Is it possible to model the interaction between spring and object by the decomposed xx-component of the spring?

If you are asking about the stiffness ( or spring constant $k$ ) , then obviously it cannot split into x and y components, because $k$ is a scalar constant. Suppose in your example, if the spring , at an angle $\alpha$ from x axis in $2D$ travels a distance $r$ then the displacement and force can be split into x and y component. That is, now the equation of such system is $$F=-kr$$
this can be split into $$F_x=-kx$$
and $$F_y=-ky$$ as $k$ is a scalar. You can connect these three equations using
$$F=\sqrt{F_x^2+F_y^2}\\ r=\sqrt{x^2+y^2}$$