Determine the frequencies

Ali Bahrain

two small gears are attached to shaft that is supported by the self-aligning bearings A and B. the enginner designing the system would like to determine the natural frequencies of the system experimentally but dose not have the equipment necessary to do so.
therefore, rather than ontaining vibration measurements, he applies a 20 lb static load at gear 1 and measures the static deflections of the shaft at the location of the center of each gear as shown in part b. he than applies a 20 lb force statically at gear 2 and again measures the static deflections of the shaft at the location of the center of each gear as shown in part c.
determine the frequencies and mode shapes