$7\mathrm{.}10\mathrm{.}1$ WP A viscous fluid is contained between wide, parallel plates spaced a distance $h$ apart as shown in Fig. P$7\mathrm{.}10\mathrm{.}1.$ The upper plate is fixed, and the bottom plate oscillates harmonically with a velocity amplitude $U$ and frequency $.$ The differential equation for the velocity distribution between the plates is

$\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{t}}=\frac{de{l}^{2}u}{del{y}^2}$

where $u$ is the velocity, $t$ is time, and $$ and $$ are fluid density and viscosity, respectively. Rewrite this equation in a suitable nondimensional form using $h,U,$ and $$ as reference parameters.