Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Welcome to Physics SE! Please be clear about what you are asking so that the community can help you. Provide sufficient details (figures, variables to use , the quantity you want to compute etc.) and your attempt or ideas regarding solving the problem.
Are you sure that relation for velocity is right? I think it should have some periodic structure to reflect the fact that the comet is going around the sun periodically.
How fast oscillations in an over damped system dies off is given by the damping ratio. It depends on both the stiffness and the damping coefficient. Check (en.wikipedia.org/wiki/Damping#System_behavior) for the complete analysis.
Practically there will be both stiffness and damping in a spring. But in theory they are separate phenomena. I am not aware of any relation connecting stiffness and damping of actual springs. It might depend on the material used etc.
Can you make it clear how you think that stiffness can be used to explain damping? Damping requires energy loss and if you consider a spring system with no damping but a finite stiffness then you will see that the energy is converted from KE of the mass to PE of the spring in a periodic way.
