Experimentally, analytically, and numerically find the natural frequencies (or modes) of the rig with minimal percent errors. This must be done in a static and rotational reference frame in order to determine the critical speeds of the rotating disk-shaft system (the rotational velocity of a system when it rotates at a frequency exciting one of its natural frequencies). Maintaining a constant disk mass of 1.12 kg, determine and analyze the effects that varying disk geometries have on the mode shapes and corresponding frequencies of the rig. Make calculated predictions about how different disk shapes affect the behavior of the rig. Determine safe ranges of operational rotation for rotors with similar disk geometries and effective shaft lengths.