Mathematically the differential equation mx"+ cx+ kx= f(t) gives an "oscillatory" solution as long as the discriminant c^{2} 4mk< 0. A "damped" oscillation is one in which c> 0. A "forced" oscillation is one in which f(t) is not identically 0.
No, in that sense, "damped" and "forced" are completely independent.
