A shaft with negligible mass is simply supported by two bearings. When a gear with a mass of 7 kg is attached to the shaft at location 1, the first critical speed is measured as 1 200 rad/s. After a second identical gear is attached to the shaft at location 2, the first and second critical speeds of the shaft are measured as 500 rad/s and 1 800 rad/s, respectively. Using the exact solution to the first and second critical speeds of a rotating shaft, determine the four influence coefficients of this shaft.