for question no.2, it should be solved in Matlab software,

Problem The output shaft of a gearbox connected to a gasoline-engine-powered air compressor is shown in Fig. 1. You may assume a 10 -inch spur-gear diameter, a pressure angle =20, and that the keyseat is cut with standard endmills. The material is AISI 1020 cold-drawn steel. a. The shaft design proposed for this application is displayed in Fig. 2. Determine reasonable sizes for the output shaft by calculating the shaft strength at the critical locations using the DE-Goodman failure criterion and assuming a design factor of 3.0. The time-varying torque on the output shaft is displayed in Fig. 3. Figure 1 b. The shaft is simply supported in deep-groove ball bearings with centers at points O and A. The effective center of the gear for force transmission is at point G. Calculate the slope at points O,A, and G and check that the calculated slopes do not exceed 0.001 radians. If any of the slopes exceed the maximum allowable values, make appropriate changes to bring them all within the limits. Figure 2 Figure 3