A uniform, elastic circular rod of length L is compressed by equal and opposite forces F...

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A uniform, elastic circular rod of length L is compressed by equal and opposite forces F applied to both ends. Determine the vibration resulting from the sudden removal of the forces. Solve this Initial Conditions problem. Hint: Use the I.C.'s in the general form as presented in case for the Euler-Bernoulli's beam vibrations. Use Lagrangian approach and the general solution for the displacement function: u(x, t) = n1 Pn (x) {an cos wnt + bnsinwnt}. Find an and bn. Please use the following I C's F EG + 14 Hint for IC's: M(x,0) = 2 EA - olx → K L Fx EA ur u (x, t) A T const. const. = A= const. H H = (2-x) EA t=0 A uniform, elastic circular rod of length L is compressed by equal and opposite forces F applied to both ends. Determine the vibration resulting from the sudden removal of the forces. Solve this Initial Conditions problem. Hint: Use the I.C.'s in the general form as presented in case for the Euler-Bernoulli's beam vibrations. Use Lagrangian approach and the general solution for the displacement function: u(x, t) = n1 Pn (x) {an cos wnt + bnsinwnt}. Find an and bn. Please use the following I C's F EG + 14 Hint for IC's: M(x,0) = 2 EA - olx → K L Fx EA ur u (x, t) A T const. const. = A= const. H H = (2-x) EA t=0