Model the three degree of freedom system shown in Figure Q5 and solve for the displacements of the three masses due to a force of 10 N applied to the bottom mass at a frequency of 20 rad/s.

(a) First establish the 3x3 mass, stiffness and damping matrices.

(b) Use the mass and stiffness matrices to evaluate the three undamped natural frequencies of the system and associated mode shapes. The mode shapes must be normalised so that the largest value in the vector is 1. (It is recommended that you use MATLAB for this analysis.)

(c) Use the mode shapes to find the principal masses, principal stiffnesses, and damping factors for the three modes.

(d) Hence find the response of the three masses by modal superposition, i.e. the displacement amplitudes.