$4\mathrm{.}18$ Consider the diving platform that is shown in Figure E$4\mathrm{.}18.$ The damping factor

associated with this platform, which is made from reinforced concrete, is $0\mathrm{.}012,$

and the first natural frequency of the platform$-$slab vibrations is designed to be

$12Hz.{?}^{18}$ When a diver jumps off this platform, an initial displacement of $1$ mm

and an initial velocity of $0\mathrm{.}1\frac{m}{s}$ are induced to the platform. Determine the

resulting vibrations.

Figure E$4\mathrm{.}18.$