3. (14 total points) The harmonically forced three-mass system below is modeled in matrix form as M + Cx + Kx = F(t) with symmetric matrices M and K, and proportional damping (Rayleigh, not shown in diagram) such that matrix C = M + BK, where a = 0.32 sec-1 and B = 0. The modal coordinate vector q is defined through x = Pq. where P = [$1$2. $3] When m = 3 kg and k = 48 N/m modal frequencies are given as 01 = 4 rad/sec and on = 8 rad/sec, and 3 = 45 rad/sec, and normalized modal vectors and modal frequencies are given as $1 = () (1) 0 The forcing vector is F(t) = 1) F(t). (a) (3 pts) Write the differential equation of motion of the third modal coordinate, 93. 4m 2. 2 = 2m Jn [20 2m 5k (0) - (2) $3 = 4/3m X Bmw2m 3k 3k 31 5k