This is, you say, a "mass-spring system" so k is the "spring constant" and c is the "coefficient of friction" (which should be negative since friction will act against velocity).
I am good at Matlab programming but over here I am stuck in the maths of the problem, I am dealing with the differential equation of spring mass system
where x’’=dx2/dt2 and x’=dx/dt. I have the values of mass and I also have the array of time and x i.e x is given for a particular value of time so I can find x’’ and x ‘ easily. I am stuck at what method to apply to find the value of c and k. I can program any method but have searched several books but didn’t get how to find c and k. If I get to know the method I can program it easily.