The partial differential equation (PDE) governing free vibrations of a uniform Euler–Bernoulli beam is given by: EI ∂⁴w/∂x⁴ + m ∂²w/∂t² = 0, where EI is the flexural stiffness, m is the mass per unit length, w(x, t) is the bending displacement, x is the coordinate along the beam length, t is time, and L is the beam length. To solve the PDE, the number of boundary conditions (BC) and initial conditions (IC) needed are