We consider the random damping harmonic oscillator in presence of external noise. The noises, representing external and internal perturbations, are modeled as an Ornstein-Uhlenbeck process or a white noise and as a dichotomous process or a white noise, respectively. Using dynamical systems tools, we analyze the expected value as well as the dispersion of the stochastic harmonic oscillator s position and velocity, presenting analytical and numerical results. In particular, we also provide expressions for the low-order expansion in the correlation time of the internal perturbation, in the case the dichotomous noise is at play. Using random damped harmonic oscillator model as a reference, we conclude by investigating the intra-day Brazilian stock price series.