Complete the following for the torsion vibration of a free-free cylindrical beam. The beam's diameter is \(15 \mathrm{~mm}\) and it is \(480 \mathrm{~mm}\) long. The beam material is 6061-T6 aluminum with \(ho=2,700 \mathrm{~kg} / \mathrm{m}^{3}, E=70 \mathrm{GPa}, v=0.35\), \(G=E / 2(1+v)\), and \(\eta=0.002\).
(a) Plot the torsion FRF over a frequency range of \(10,000 \mathrm{~Hz}\). Use a semilogarithmic scale.
(b) How many modes are captured in this bandwidth (excluding the rigid body mode)?
(c) What is the natural frequency of the first (non-rigid) torsion mode?