Replacing Simscape's gimbal joint's Spring Stiffnes with External Torque

Hello,

I tried to understand how gimbal joint's Spring Stiffnes work, so I tried to replace the Spring stiffness with external torque and the results are not equal.

Here is what I tried:

This is a 3D pendulum with gimbal joint. The upper gimbal joint has 3 spring with stiffnes k for all the coordinates (x,y,z). The lower gimbal joint's spring stiffnesses are zero but there is an External torque with the value of -k*coordinate acting on the following body (this I thought would replicate the springs in the gimbal joint) as shown in the following figure.

When I simulate the pendulum such that it rotates only around one axis it works perfectly and there is 0 error between the upper and lower model. However, when I try to simulate a general motion then there is error between upper and lower model. I tried to set the external torque resolution frame both to World and Attached Frame but I just couldn't figure out how to replicate the springs with external torque.

Do you have any idea or link to how the Springs in the gimbal joint works ? Thank you, Ondrej.