We demonstrate the resonant-like behaviour of the cardiopulmonary system in healthy people occurring at the natural low frequency oscillations of 0.1 Hz, which are often visible in the continuous pressure waveform. These oscillations represent the spontaneous oscillatory activity of the vasomotor centre and are sometimes called the Mayer waves. These 10-second rhythms probably couple with forced breathing at the same frequency and cause the observed cardiopulmonary resonance phenomenon. We develop a new method to study this phenomenon, namely the averaged Lomb-Scargle periodogram method, which is shown to be very effective in enhancing common frequencies in a group of different time series and suppressing those which vary between datasets. Using this method we show that in cardiopulmonary resonance the cardiopulmonary system behaves in a very similar way to a simple mechanical or electrical oscillator, i.e. becomes highly regular and its averaged spectrum exhibits a clear dominant peak and harmonics. If the forcing frequency is higher than 0.1 Hz, the total power and the share of power in the dominant peak and harmonics are lower and the prominence of the dominant peak and its harmonics greatly diminishes. It is shown that the power contributions from different forcing frequencies follow the resonance curve.