The rubber springs of a tuned mass damper (TMD) exhibit both nonlinear stiffness and damping, which complicates measurements of the frequency response function (FRF) of the device. In this paper we model and compare the frequency responses measured with both impulse hammer excitation and a shaker base excitation method. Since the impulse response will spend only a short time in the nonlinear regime, a reasonable assumption is that the nonlinearities will be less apparent and more difficult to determine. The results show that this is not the case and that both methods yield similar nonlinear parameters. By comparing responses at different excitation levels with appropriate nonlinear models, the nonlinearities can be determined. The results indicate that these approximations of the nonlinear effects are able to describe the dynamic behaviour of the TMD, and that the nonlinear properties of the material differ somewhat in the two measurement situations.