The work in this thesis was submitted to The University of Manchester for the degree of Doctor of Philosophy in September 2016 by Morgan Timothy Hibberd and is entitled "Studying low frequency vibrational modes using ultrafast techniques".In this thesis, I report on the investigation of the low frequency vibrational modes in a number of different systems using ultrafast spectroscopic techniques. These consist of biological systems, including the enzyme, morphinone reductase (MR) and the related biomolecules, riboflavin (Rb) and flavin mononucleotide (FMN), as well as non-biological systems, including the semiconductor gallium nitride (GaN) and gold nanoparticles (Au NPs). The term low frequency refers to terahertz (THz) frequencies, where vibrational modes exist at the molecular level, with molecular rotations, lattice vibrations and inter- and intra-molecular vibrations occurring in the THz spectral range. These vibrational modes occur on sub-picosecond timescales and therefore ultrafast techniques utilising femtosecond laser pulses provide a means of studying these modes, and are employed throughout this thesis.The two ultrafast techniques of transient absorption (TA) spectroscopy and terahertz time-domain spectroscopy (THz-TDS) were used. Firstly, a high-repetition rate transient absorption (HRRTA) spectrometer was commissioned to perform pump-probe measurements with an ultraviolet pump and broadband visible probe. The performance of the HRRTA spectrometer was benchmarked using Au NPs and used to investigate the existence of a promoting vibration in MR contributing to the catalysis process, predicted to occur at THz frequencies. Weak oscillations were detected in the charge-transfer absorption band of MR bound to the non-reactive cofactor 1,4,5,6-tetra-hydro-nicotinamide adenine dinucleotide (NADH4), with a frequency of approximately 1.5 THz and provide evidence of the first direct observation of a promoting vibration in an enzyme.To complement the TA measurements, THz-TDS was also used to obtain direct measurements of the absorption at THz frequencies. Due to the challenge of studying water-based biological samples, an initial investigation was performed on a wurtzite GaN wafer, which exhibited optical phonon modes in the THz frequency range that were found to determine the dielectric response of the semi-insulating semiconductor wafer. Use of a non-polar m-plane wafer allowed the anisotropic nature to be observed and values of 9.22 ± 0.02 and 10.32 ± 0.03 for the static dielectric constants were obtained for the THz electric field polarised both perpendicular and parallel to the c-axis of the wurtzite GaN wafer, respectively. Finally, biological studies using THz-TDS were performed with measurements on Rb pellets and films revealing vibrational modes in the THz region. The sharp absorption features were not observed in FMN, despite a small difference in molecular content from Rb, and dehydration was required to reveal small amplitude absorption features. Final measurements on MR and MR-NADH4 films were carried out and evidence of absorption features in the THz frequency range were observed, however further work is required to determine the precise origin of these features.