Consider the uniform beam is subjected to an initial displacement distribution with respect to its original position: Please drive eq2 from eq1 The exact solution for the natural frequency of the r-th mode is: W = (rad/s) r = 1, 2,... = (TT) MLA where E is Young's modulus, and I is the moment of inertia of the beam u2(x1, x2, t = 0) = A (2/17 - 22/1/3 + 1/1(1) ( eq1 1 (2 + 1) sin n=0 (2n+1)5 cos(nt) eq2 L X2 96A u2(x1, x2,t): = X1 E,I,m where n = [(2n + 1)] EI mL4 (rad/s) n = 0, 1, 2,...