A robot arm is \(60 \mathrm{~cm}\) long, made of a material of elastic modulus \(200 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\), and has the cross section of Figure P8.18. The total mass of the arm is \(850 \mathrm{~g}\). A tool of mass \(1 \mathrm{~kg}\) is attached to the end of the arm. Assume one end of the arm is pinned and the other end is free. Use a three degree-of-freedom model to determine the arm's natural frequencies.

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6 mm FIGURE P8.18 8 mm 1 mm