and the parallel resonant frequencies together determine an important metric of resonator performance the resonator coupling coefficient k 2 a commonly used equation that relates k 2 to fs and fp is k 2 pi 2 fs fp cot pi 2 fs fp fig9 illustrates that there is no appreciable change in the value of k 2 when the series resonant frequency is adjusted by the method described above because the parallel resonant frequency tracks with the series resonant frequency fig1 is a plot of the measured change of resonant frequency of a 200 um by 200 um resonator based on the resonator illustrated on fig6 this figure expresses in mhz the same result shown in fig9 fig1 is a cross section and top view of a resonator 130 with a reflowable material 74 used as the mass load layer before and after the reflow operation before the reflow holes 78 are visible in the reflow layer after reflow the holes are no longer visible with an attendant reduction in the overall reflow material 74 mass load layer thickness fig1 is a plot of the simulated frequency response of the resonator with a reflowable material 74 of fig1 the effect of two different hole densities in the reflow material results in a different secondary acoustic path 50 for the resonator before and after reflow the resonant frequency 135 before reflow is higher than the resonant frequency 136 after reflow some additional aspects of the present invention are described below in one embodiment an array of resonators is provided the resonators have a portion that converts electrical energy to mechanical energy or mechanical energy.