A turbomachine engine includes a fan section having a fan shaft, and a core engine having one or more compressor sections, one or more turbine sections that includes a power turbine, and a combustion chamber in flow communication with the compressor sections and turbine sections. The turbomachine engine includes a low-speed shaft coupled to the power turbine and having a midshaft that extends from a forward bearing to an aft bearing. The low-speed shaft is characterized by a midshaft rating (MSR) between two hundred (ft/sec)1/2 and three hundred (ft/sec)1/2. The low-speed shaft has a redline speed between fifty and two hundred fifty feet per second (ft/sec). The turbomachine engine includes a gearbox assembly that couples the fan shaft to the low-speed shaft and characterized by a gearbox assembly mode less than 95% of a midshaft mode of the midshaft or greater than 105% of the midshaft mode.