The basic equation that describes the motion of the fluid above a large oscillating flat plate is

\[ \frac{\partial u}{\partial t}=v \frac{\partial^{2} u}{\partial y^{2}} \]

where \(u\) is the fluid velocity component parallel to the plate, \(t\) is time, \(y\) is the spatial coordinate perpendicular to the plate, and \(v\) is the fluid kinematic viscosity. The plate oscillating velocity is given by \(U=U_{0} \sin \omega t\). Find appropriate dimensionless parameters and the dimensionless differential equation.