Consider the gear shaft system in Figure P1.9. The length and the diameter of shaft \(A\) are \(50 \mathrm{~cm}\) and \(4 \mathrm{~cm}\), respectively. Similarly, the length and the diameter of shaft \(B\) are \(60 \mathrm{~cm}\) and \(3 \mathrm{~cm}\), respectively. Masses of gears A and B are \(1.5 \mathrm{~kg}\) and \(0.5 \mathrm{~kg}\), respectively. The gear ratio is 2.

Figure P1.9 

Assuming that the shaft material is steel, determine the equivalent mass and the equivalent stiffness with respect to the angular displacement of gear \(\mathrm{A}\). What is the natural frequency?

Transcribed Image Text:

Shaft A Gear B Shaft B Gear A