Do you mean you have a coil spring in a physical prototype and you are trying to model it in an ANSYS model? If you are doing a Static Structural model, you can use a damping value of 0.
You can measure the stiffness by using the following method. Hang the spring from a hook, and hang a small weight that will pull the spring to a small extension. Find a second weight and a scale to measure that weight accurately, convert to newtons and call that value F. The second weight should pull the spring near to its working length. Put some tape around the bottom hook and put a horizontal line as a fiducial of the displacement of the end of the spring. Get a mm scale and support that behind the tape and fiducial so you can read out the current position of the end of the spring. Now hang the second weight from the first and measure the displacement of the end of the spring from its position with the first weight and call that displacement value X.
Calculate the stiffness of the spring K = F/X in N/mm.