An important aim of nanoparticle research is to understand how the properties of materials depend on their size and shape. In this thesis, time-resolved spectroscopy has been used to measure the physical properties of nanometer sized objects, such as the characteristic time scale for heat dissipation and their elastic moduli. In our experiments, metal nanoparticles are excited with a sub-picosecond laser pulse, which causes a rapid increase in the lattice temperature. In the first project, the rate of heat dissipation from Au nanoparticles to their surroundings was examined for different size gold nanospheres in aqueous solution. Laser induced lattice heating can also impulsively excite the phonon modes of the particle that correlate with the expansion co-ordinates. For spherical Au particles the symmetric breathing mode is excited. Experimental results for ~50 nm diameter Au particles were compared to a model calculation where the expansion coordinate is treated as a damped harmonic oscillator. This gives information about the excitation mechanism. In the second project, the extensional and breathing modes of cylindrical gold nanorods were studied by time-resolved spectroscopy. These experiments yield values for the elastic constants for the rods. Both the extensional mode and the breathing mode results show that gold nanorods produced by wet chemical techniques have a smaller elastic moduli than bulk gold. HR-TEM and SAED studies show that the rods have a 5-fold twinned structure with growth along the [110] crystal direction. However, neither the growth direction nor the twinning provide a simple explanation for the reduced elastic moduli measured in the experiments. In a final project, polydisperse silver nanoparticle samples were investigated. A signal due to coherently excited vibrational motion was observed. The analysis shows that the observed signal arises from the triangular-shaped particles, rather than the rods or spheres that are present in the sample. The triangles dominate the response because they have a much narrower size distribution than the rods.