We consider a wavelet analysis of various time series of the position for a Morse oscillator which is weakly forced and weakly damped. We focus on the highly anharmonic regime (close to the dissociation energy) where the time series are highly aperiodic and chaotic. In this regime, there are many significant frequency components in a Fourier expansion of the time series. Consequently, the usual Fourier analysis is problematic since it is assumed that the time series are stationary. Our aim is to show that a wavelet analysis can be used to determine quantitatively multiple forcing frequencies. The utility of a wavelet analysis is due primarily to the localization of the orthogonal wavelet basis functions in both frequency and time.