Write and sub in to pde.
Beam's dynamic deflection is governed by the following PDE
EI(∂^4w/∂x^4)+(rho)*A* (∂^2w/∂t^2)=f(x,t)
where E = the modulus of elasticity, I = the moment of inertia, p = mass density, A = cross-section area, w(x,t) = deflection, 0 ≤ x ≤ L = axial coordinate, L = length, t = time. The load is given as the following function
f(x,t) = sin(pi*x/L)sin(omega*t)
Use separation of variable and the normal mode approach to find w(x,t) if the boundary conditions are
w = 0 at x = 0 and x = L;
∂^2w/∂x^2=0
And the initial conditions read w=O,
∂w/∂t =0 at t =0