Use a one-element, finite-element model to approximate the lowest torsional natural frequency of a uniform shaft with
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Use a one-element, finite-element model to approximate the lowest torsional natural frequency of a uniform shaft with a length \(L\), polar moment of inertia \(J\), is made from an elastic material of density \(ho\), and has a shear modulus \(G\) that is fixed at one end and has a torsional spring of stiffness \(k_{t}\) at its other end.
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