One of the very current problems in the field of nonlinear forced oscillations are oscillations due to low frequency excitation. This type of excitation is present, both in engineering systems and in nature. Good understanding and detection of these oscillations has multiple benefits. For example, low and ultra low frequency signals usually procede an earthquake, so their detection is important in the early detection of this phenomenon. In addition, low frequency signals can be used to detect damage within structural objects during their service life. Also, nature and engineering structures abound with low-frequency oscillatory motions, which today attracts the attention of researchers in the field of energy harvesting. However, in contrast to forced oscillations with excitation above 1Hz which has been very well studied in previous decades, the low-frequency regime still much less explored. Here, a new mathematical model of a nonlinear externally excited oscillator will be presented and its connection with the parametrically excited Duffing oscillator will be shown. The connection is established by considering the bursting oscillations ond phase transitions in the Duffing oscillator. Regular and irregular types of bursting oscillations are observed in the Duffing oscillator. A detailed explanation is given based on the consideration of two-stage fixed point bifurcation which includes a modified version of supercritical pitchfork bifurcation and supercritical cusp bifurcation. Supercritical cusp bifurcation, which occurs periodically at times when the restoring force in the Duffing oscillator becomes pure nonlinear is considered in a toplogically equivalent space. These considerations in Duffing’s parametrically excited system are used to understand the behavior of the newly introduced externally excited system. It is shown that in this model, the characteristic bursting like behavior from the Duffing system can be easily and clearly used to detect the presence of external excitation in the low and ultra low frequency regime. In addition to the mathematical model, all this is demonstrated on a real base excited mechanical model that contains a low frequency pendulum mechanism. The conditions under which this mechanical model can be represented as a parametrically excited Duffing oscillator are shown. In this way, a certain analogy can be established with the Mathieu’s oscillator which has a mechanical explanation in the oscillation of the simple pendulum whose support periodically moves.