Due to its symmetry properties, second-harmonic generation in plasmonic nanostructures enables the observation of even-parity modes that couple weakly to the far field. Consequentially, those modes radiate less and thus have a longer lifetime. Using a full-wave numerical method, we study the linear and second harmonic dynamical responses of a silver nanorod under plane-wave femtosecond pulse illumination. Depending on the spectral position and duration of the pulse, the decaying field of the different modes can be separated, and the free oscillations of each mode are well fitted by a damped harmonic oscillator model, both in the linear and nonlinear regimes. Additionally, interference effects between different modes excited at the second harmonic are observed.