A root manipulator is (60 mathrm{~cm}) long, made of steel (left(E=210 times 10^{9} mathrm{~N} / mathrm{m}^{2} ight.),

A root manipulator is \(60 \mathrm{~cm}\) long, made of steel \(\left(E=210 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\right.\), \(ho=7500 \mathrm{~kg} / \mathrm{m}^{3}\) ) and has the cross section of Figure P10.35. One end of the manipulator is fixed and a 1-kg mass is attached to its opposite end. Determine the three lowest natural frequencies for transverse vibration of the manipulator.

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+ -10 mm t = 1.5 mm FIGURE P10.35 15 mm