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.