Engineers use the device shown to measure an astronaut’s moment of inertia. The horizontal...

Engineers use the device shown to measure an astronaut’s moment of inertia. The horizontal board is pinned at O and supported by the linear spring with constant k = 12 kN/m. When the astronaut is not present, the frequency of small vibrations of the board about O is measured and determined to be 6.0 Hz. When the astronaut is lying on the board as shown, the frequency of small vibrations of the board about O is 2.8 Hz. What is the astronaut s moment of inertia about the z axis?