$*22-28.$ The platform $AB$ when empty has a mass of $400$ kg $,$

center of mass at $G_1,$ and natural period of oscillation

${}_1=2\mathrm{.}38s.$ If a car, having a mass of $1\mathrm{.}2$ Mg and center of

mass at $G_2,$ is placed on the platform, the natural period

of oscillation becomes ${}_2=3\mathrm{.}16s.$ Determine the moment

of inertia of the car about an axis passing through $G_2.$