The principal normal stress \(\sigma\) due to forcing of a beam with a concentrated harmonic excitation is a function of

\(F_{0}\), the amplitude of loading

\(\omega\), the frequency of the loading

\(E\), the elastic modulus of the beam

\(ho\), the mass density of the beam

\(A\), the beam's cross-sectional area I, the beam's cross-sectional moment of inertia

\(L\), the beam's length

a, the location of the load along the axis of the beam Present different problems that are to be formulated in nondimensional form. For each problem answer the following.

(a) What are the dimensions involved in each of the parameters?

(b) How many dimensionless parameters does the Buckingham Pi theorem predict are in the non-dimensional formulation of the relation between the natural frequencies and the other parameters?

(c) Develop a set of dimensionless parameters.