Ah I see thank you that works. As a quick follow up question, my next line of code is this, and I seem to get some new errors. Would you mind taking a look at it? (I am assuming you do not need dampdata to debug the code?)
nlm = NonlinearModelFit[dampdata,
ArcTan[(dl Sum[Sin[model[cd, kvc][[k]][[0]][t]], {k, NN}])/(
dl Sum[Cos[model[cd, kvc][[k]][[0]][t]], {k, NN}])], {cd, kvc}, t,
Method -> "Gradient"]
