We have implemented a rapid scanning technique into THz time-domain spectrometers using an oscillating frictionless delay line, especially adapted for nonlinear THz experiments. Thereby we were able to increase the dynamic range of THz measurements in the frequency range from 40 to 200 cm by up to 24 dB and reduce the scanning time by up to a factor of 200. We report here test measurements on TDS-setups at repetition rates of 80 MHz and 5 kHz. The dynamic range exceeds 64 dB, which allows to record even small changes in the THz absorption upon optical excitation by a THz probe, covering the frequency range of the intermolecular modes and the phonon bands. We demonstrate the potential of this technique for optical-pump THz-probe experiments using a 70 μm thick high-resistivity silicon, excited by 400 nm, ∼50 fs pulses as a sample.