Dynamic Kerr effect measurements provide a simple realization of a nonlinear experiment. We propose a field-off experiment where an electric field of one or several sinusoidal cycles with frequency Ω is applied to a sample in thermal equilibrium. Afterwards, the evolution of the polarizability is measured. If such an experiment is performed in the terahertz range it might provide valuable information about the low-frequency dynamics in disordered systems. We treat these dynamics in terms of a Brownian oscillator model and calculate the Kerr effect response. It is shown that frequency-selective behavior can be expected. In the interesting case of underdamped vibrational motion we find that the frequency dependence of the phonon damping can be determined from the experiment. Also the behavior of overdamped relaxational modes is discussed. For typical glassy materials we estimate the magnitude of all relevant quantities, which we believe will be helpful in experimental realizations.