Question about Physics Constraints Damping

I am attempting to create a “taffy-like” physics constraint. To understand what I mean, imagine two spheres constrained together to create a pendulum. The anchor sphere is static (not a physics body) and placed in mid-air, while the pendulum sphere is placed directly below it and set to simulate physics. When the simulation begins, the pendulum sphere will react to gravity and drop. At this point, what I hope will happen is- when the pendulum reaches it’s linear limits, it gently slows to a stop. What actually happens is- it drops and jerks to a stop much too abruptly.

This is the best I can get after hours of trying different settings: ball dropping fail - YouTube

My question is: is it even possible to achieve what I have described using physics constraints? If so, is there a mathematical formula one can use to get just the right settings (i.e. mass of object vs. downward force vs. constraint stiffness and damping)? If it is not possible, does anyone have a suggestion as to how to achieve such an effect? Thanks in advance for your insight…

I should also add, I have tried using the linear motor, but that produces more of a bounce (at least using the settings I tried). I am after a soft deceleration, not a bounce.