As shown in the figure below, the length of a simply supported beam is I, the bending stiffness is El, and the mass per unit length is pa(Ro*a). It is acted upon by simple harmonic force f(x,t) = fo sin w t at x =a. 1) List the transverse microvibration equations and boundary conditions of the beam; 2) Derive the natural frequency and modal function of the beam; 3) Apply the modal superposition method to solve the steady-state response of the beam. a fo sin cot 1