Out-of-balance A common source of excitation force is a rotating system with an out of balance mass. As shown in the diagram this is a mass m' at a radius r rotating with an angular velocity w. To be realistic it is also important to include an angular acceleration a as the steady angular velocity is not achieved instantly. It can be shown that the force F(t) that acts on the mass m as a result of the rotating out of balance mass m' is and the equation of motion becomes and rearranging There are several areas of interest. What happens as the rotation starts up? What happens at constant speed?

NOTE: There will be a force on the mass perpendicular to the x direction. However as this is a one degree-of-freedom system, this force does not produce any motion. In practice the constraint, that only allows motion in the x direction, will be subject to a force that is perpendicular to the x direction.