Using a femtosecond pump-probe technique, the fundamental mechanical radial mode of silver nanoparticles is coherently excited and probed via its interaction with the electron gas. The mechanical oscillations are launched by an indirect displacive process and are detected via the induced modulation of the surface plasmon resonance frequency. The measured fundamental radial mode period and damping time are found to be proportional to the nanoparticle radius in the range of 3-15 nm, in agreement with theoretical predictions.