We experimentally investigate the usefulness of nonlinear springs in a MEMS electrostatic energy harvester under colored noise vibrations. The experimental characterization of the energy harvester using nonlinear springs is compared with analytical and simulated results for an energy harvester with linear springs. For random vibrations with a bandwidth of 50 Hz and varying center frequencies, we found that the maximum output power of the nonlinear-spring harvester is 1.7 times lower than that of the linear-spring harvester, but the 1-dB bandwidth is two times larger. For vibration center frequencies of 38 Hz and 58 Hz below the resonant frequency, the nonlinear-spring harvester always achieves more power than the linear-spring one regardless of the vibration bandwidth. By varying the bias voltage, we found that the nonlinear-spring harvester obtains an average power of about 1 μW at 180 V, corresponding to an efficiency of 92% for a white noise excitation of 7.29 x 10-4 g²/Hz and 1.2 μW at 36 V for a frequency down-sweep at 0.15 g. A design variety of the device reached an output power of 7 μW at 120-V bias and 0.36-g acceleration.