This is Mathematical Modeling problem~

plz solve it

5: The beam equation describes the motion of a solid, homogeneous beam. The deection of the beam at some point I along it's length, at time t is n(:e,t), and is described by 64a 621: Elm + \"m \"I where E is the elastic modulus of the beam (dimensions ML'IT'E), n is the deection {units L), a: is position along the beam (units L), n is the linear densityr (mass per unit length) of the beam (units ML\"), and t is time (units T). The initial conditions are an u(:c,{})U, EUattU, and the boundary conditions are . 3% 3n n{,t) =nosm(wt), a - at :1: 0, n(i,t) -U, a [l atxI. (a) Find the dimensions of I, the second moment of inertia of the beam. (b) Nondimensionalise the beam equation, and choose appropriate scales so that there are no dimensionless groups left in the boundary conditions