The effect of rotation on the steady state response of a spring-mass system under harmonic excitation

A two degree-of-freedom system, consisting of a point mass which is constrained to move in one plane, is considered. The motion is controlled by linear springs and viscous damping. A constant amplitude harmonic force is applied along one axis in the plane, which is rotating at a constant angular velocity about an axis perpendicular to the plane. Due to the rotation, oscillation takes place in the direction perpendicular to, as well as along, the axis of excitation.The amplitude and phase of the steady state vibrations are derived as a function of the excitation frequency and the rate of turn. For rates of turn very much less than the system natural frequencies, this theory covers the principles of vibratory rate sensors such as the tuning fork; however, the emphasis here is on the performance of the system when the angular velocity is of the same order as the natural frequencies of the system.