I can still address your question regarding the relationship between the direction of spring deformation and the direction of the spring force.
In a typical helical (coil) spring, the direction of deformation refers to the displacement or compression of the spring along its axis. When a spring is compressed or stretched, it exerts a force that opposes the deformation and tries to restore its original shape. This force is commonly referred to as the spring force or the restoring force.
According to Hooke's Law, the spring force is directly proportional to the displacement of the spring. In mathematical terms, this can be expressed as F = -kx, where F represents the spring force, k is the spring constant (a measure of the stiffness of the spring), and x represents the displacement from the equilibrium position.
The negative sign in the equation indicates that the spring force acts in the opposite direction to the displacement. If the spring is compressed (negative displacement), the spring force will be directed outward to restore the spring to its equilibrium position. On the other hand, if the spring is stretched (positive displacement), the spring force will be directed inward, again aiming to bring the spring back to its equilibrium state.
Thus, the direction of the spring force is determined by the direction of the deformation. When you push or pull a spring, the force it exerts will always be in the opposite direction to the displacement, in line with Hooke's Law.