2. Dimensional analysis can be used in problems other than fluid mechanics ones. The important variables affecting the period of a vibrating beam (usually designated as T and with dimensions of time) are the beam length , area moment of inertia J, modulus of elasticity E, material density , and Poisson's ratio a, so that T = fen(t,1,E,p,0) Recall that the modulus of elasticity has typical units of N/m\" and Poisson's ratio is dimensionless. (a) Find dimensionless version of the functional relationship. (b) If E and J must always appear together (meaning that EI is effectively a single variable), find a dimen- sionless version of the functional relationship