Exact analytical operator solutions of the interacting model of a single quantized (non-dissipative) harmonic oscillator (HO) with a train of n-chirped Gaussian pulses are derived in terms of the error function of complex argument. Explicit expressions are then calculated and examined computationally for the average photon number of the HO and the emitted spectrum. The chirp parameter (c) induces non-sinusoidal oscillations that lead to: (i) 'step-like plateau' in the dynamics of the average photon number with both n, τ R (repetition time) large, and, (ii) a 'hole burning' profile and asymmetrical ringing in the spectrum, depends on the initial state of the HO.