  Exact relaxation times and eigenfunctions for a simple mechanical model of
polymer dynamics are obtained using supersymmetry methods of quantum mechanics.
The model includes the finite extensibility of the molecule and does not make
use of the self-consistently averaging approximation. The finite extensibility
reduces the relaxation times when compared to a linear force. The linear
viscoelastic behaviour is obtained in the form of the ``generalized Maxwell
model''. Using these results, a numerical integration scheme is proposed in the
presence of a given flow kinematics.
