In the recent work of Nakariakov et al. (2004), it has been shown that the time dependences of density and velocity in a flaring loop contain pronounced quasi-harmonic oscillations associated with the 2nd harmonic of a standing slow magnetoacoustic wave. That model used a symmetric heating function (heat deposition was strictly at the apex). This left outstanding questions: A) is the generation of the 2nd harmonic a consequence of the fact that the heating function was symmetric? B) Would the generation of these oscillations occur if we break symmetry? C) What is the spectrum of these oscillations? Is it consistent with a 2nd spatial harmonic? The present work (and partly Tsiklauri et al. (2004b)) attempts to answer these important outstanding questions. Namely, we investigate the physical nature of these oscillations in greater detail: we study their spectrum (using periodogram technique) and how heat positioning affects the mode excitation. We found that excitation of such oscillations is practically independent of location of the heat deposition in the loop. Because of the change of the background temperature and density, the phase shift between the density and velocity perturbations is not exactly a quarter of the period, it varies along the loop and is time dependent, especially in the case of one footpoint (asymmetric) heating. We also were able to model successfully SUMER oscillations observed in hot coronal loops.