$10\mathrm{.}1310\mathrm{.}14$ The structures of Figs. P$9\mathrm{.}7$ and P$9\mathrm{.}8$ are modified so that the columns are hinged at the base. Determine the natural vibration frequencies and modes of the modified system, and compare them with the vibration properties of the original structures determined in Problems $10\mathrm{.}11$ and $10\mathrm{.}12.$ Comment on the effect of the column support condition on the vibration properties.