Question: A solid disk of diameter (30 mathrm{~cm}) and mass (10 mathrm{~kg}) is attached to the end of a solid 3-cm-diameter, 1-m-long steel shaft (left(G=80 times

A solid disk of diameter $30 \mathrm{~cm}$ and mass $10 \mathrm{~kg}$ is attached to the end of a solid 3-cm-diameter, 1-m-long steel shaft $\left(G=80 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\right)$. A torsional vibration absorber consists of a disk attached to a shaft that is then attached to the primary system. If the absorber disk has a mass of $3 \mathrm{~kg}$ and a diameter of $10 \mathrm{~cm}$, what is the required diameter of a $50-\mathrm{cm}$-long absorber shaft to eliminate steady-state vibrations of the original system when excited at $500 \mathrm{rad} / \mathrm{s}$ ?

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