Given the following image of a shaft, what is the critical speed of rotation in units of rad/s if the shaft has the following section lengths and deflections (y) and the centers of the given sections. Assume the shaft is made of steel and all dimensions are given in inches. Ignore the weight change due to the keyway. 10 x 106 in 2.8 in, y1 L1 L2 11 in, y2 300 x 106 in 15

  

L1= 2.8 in, y1 = 10 x 106 in L2 = 11 in, y2 = 300 x 106 in L3 = 2.3 in, y3 = 150 x 10 in L4 = 3.0 in, y4 = 10 x 106 in