Sub-resonant Response of a Mechanical System parametrically excited at its Resonant Frequency

IN the course of an attempt to improve the response of an inertial seismometer to very-low-frequency frame movements, it appeared worthwhile to investigate the response of a spring-mass system subjected to parametric excitation 1 . The parametric excitation or ‘pumping’ consisted of modulating the restoring force on the mass by means of an electromechanical spring 2 driven from a sinusoidal current source. In the initial work the restoring force was varied at twice the resonant frequency of the system as is usually done in a degenerate parametric device. It was found both from theory 3 and experiment that this will increase the relative motion between mass and frame only for inputs with a frequency at or near the resonant frequency, and that the input must bear the proper phase relationship to the pump. There is no improvement for frequencies much below resonance.