The differential equation for small-amplitude vibrations y(x, 1) of a simple beam is given by \rho A \frac{\partial^{2} y}{\partial t^{2}}+E I \frac{\partial^{4} y}{\partial x^{4}}=0 where p = beam material density A = cross-sectional area 1= area moment of inertia E = Young's modulus Use only the quantities p, E, and A to nondimensionalize y, x,and t, and rewrite the differential equation in dimensionless form. Do any parameters remain? Could they be removed by further manipulation of the variables?

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