A common problem in the application of normal coordinate analysis to study low-frequency modes of large molecular systems is the occurrence of a large number of negative eigenvalues (unstable modes). By averaging the terms of the Hessian matrix over a short classical trajectory, the unstable modes were found to be completely eliminated for 6000 atom model polymer particles and crystals. The time-averaged matrices were made possible by an efficient analytical formulation of the Cartesian second derivatives and diagonalization was achieved using a sparse matrix solver (ARPACK).