Figure 1 shows a shaft carrying three rotors (masses). The shaft is made of steel and has a solid circular cross-section with a diameter of 10 cm. With m 20 kg, m = 50 kg, m3 = 40 kg, 1 m, 2 = 3 m, 13 = 4 m, 4 = 2 m, E=2.07 X 1011 N/m i. determine the matrices of the system ii. determine the natural frequencies of the system iii. evaluate the fundamental frequency obtained from (ii) with that obtained from Rayleigh's method and Dunkerley's method iv. state your opinion on the accuracy and efficiency of the three methods used to solve this shaft vibration and other complex vibration problems in industry m m2 W3 W1 W2 Figure 1 m3