Problem 1: Two identical masses (m) are attached to rigid stationary walls and each other with springs kg and kc=0.5kg as shown below. Complete the following parts while showing your work and justication for full credit. lnc'll |>x6 V A B 370 F 333%??? 1:0 make mFeko J i) Choose a set of initial conditions that would result in a single frequency of free Vibrations for both masses. Express that frequency in terms of m and k0. ii) Choose a set of harmonic forces, F A and F B to the masses that would trigger resonance at only a single frequency when forcing frequencies are varied in a range that contains both natural frequencies. Express that frequency in terms of m and k0. iii) Choose a damping matrix in physical coordinates that guarantees diagonalization with modal analyses (you can express the components of the matrix in terms of m and kg). iv) Assuming that a harmonic force is applied to mass B only (F A=0), at which forcing frequency mass A acts as a perfect absorber, i.e., mass B has zero response at steadystate? Express that frequency in terms of m and k0