text: Knowing Newton’s Second Law stating force is equivalent to mass times acceleration, or , and that acceleration is the derivative of velocity, or  (characteristic speed/time) in the case of fluid mechanics, we see
  Since characteristic speed can be represented as length per unit time, , we get
  where,
  : m = mass,
  : U = characteristic speed,
  : L = characteristic length.
  Dividing both sides by , we get
  where,
  : m = mass,
  : U = characteristic speed,
  : F = net external forces,
  : L = characteristic length.
  This provides a dimensionless basis for a relationship between mass, characteristic speed, net external forces, and length (size) which can be used to analyze the effects of fluid mechanics on a body with mass. 
  If the net external forces are predominantly elastic, we can use Hooke’s Law to see
  where,
  : k = spring constant (stiffness of elastic element),
  : ΔL = deformation (change in length).
  Assuming , then . With the natural resonant frequency of the elastic system, , being equal to , we get
  where,
  : m = mass,
  : U = characteristic speed,
  :  = natural resonant frequency,
  : ΔL = deformation (change in length).
  Given that cyclic motion frequency can be represented by  we get,
  where,
  : f = frequency,
  : L = characteristic length,
  : U = characteristic speed.