Normal mode eigenvector

Consider the mechanical system with three degrees of freedom shown below. The positions of the particles are measured from their equilibrium positions. The system has a normal mode eigenvector (19.13, b, 19.13)^T.

 If all particles start from their equilibrium positions and the leftmost and rightmost particles are given a velocity of 5.77 ms^-1, the velocity of the middle particle is -48.16 ms^-1, the system will oscillate in a normal mode.

Determine the value of b, giving your answer to 3 decimal places.Consider the mechanical system with three degrees of freedom shown below. The positions of the particles are measured from their equilibrium positions. The system has a normal mode eigenvector (19.13, b, 19.13)^T.

 If all particles start from their equilibrium positions and the leftmost and rightmost particles are given a velocity of 5.77 ms^-1, the velocity of the middle particle is -48.16 ms^-1, the system will oscillate in a normal mode.

Determine the value of b, giving your answer to 3 decimal places.